Firstly, "historical" does not have to be concretely historical. That is, the author could be referring to a non-specific marriage situation. Surely it is too narrow to say that only a concrete, specific historical event can be a type. The author could simultaneously be idealizing marriage, showing us the way it ought to be.
Lane, It sounds like you are promoting a view similar to Tremper Longman's, where the characters are literary rather than literal -- the creation of the artist rather than real-life people. Might I suggest that the word "literal," which heads up this discussion, is now irrelevant. The Song cannot be considered both literal and typological, as suggested by the OP, when in fact it is not regarded as being literal. As the word "literal" is irrelevant to the discussion, my remarks, in which I answer the claim that the Song is to be taken literally, have been rendered inapplicable. I guess it was an useful mental exercise even if I was being led down the "garden" path.
It is not too narrow to require historicity as a precondition of type, because that is basic to the definition of type. I would ask you, in the interest of helpful, clarifying discussion, to please use terms with accepted hermeneutical meaning. The two elements necessary to a type are divine institution and resemblance between the type and thing signified. Your use of "type" destroys both these elements. (1.) There is no transaction in which God designates this "marriage" as a type. Your only appeal is to marriage in general, an appeal which depends on the historical enactment in the beginning. Moreover, it is accepted by those (like Longman) who make use of the canonical process approach, that there is no "marriage" in the book. Marriage can only be read into it because of its canonical positioning. (2.) An ideal cannot be a type. A type is always less than ideal and looks to something ideal to perfect it. To say that ideal marriage is in view in the Song is really to say something about the Antitype, not the type.
I think you would be better off abandoning the idea of "typology" and adopt the concept of "analogy," as in Longman's approach. A type requires similarity and dissimilarity with the Antitype. An analogy holds true while there is similarity, and ceases where there is dissimilarity.
In the final analysis, it appears that the OP must be answered in the negative, even by your own approach. The Song is neither literal nor typological, if we use those terms as they are usually understood.
Secondly, your objection with regard to the historical situation being absurd is weak. Most commentaries these days do not argue that the historical situation in view is Solomon with one of his many wives. The king language is usually interpreted these days as the woman's picture of her husband, calling him king, even if he is not an historical king.
I acknowledge what you are saying. The weakness of my statement is the result of having been misled by the word "literal" as it appears in the OP. I have distinct objections against the modern literary approach, and will attempt to make those clear in response to your fifth point.
Thirdly, the argument from the title of the Song only works if I am arguing that the Song is ONLY about human marriage, and not also about God's marriage to His people. I would argue that it is equally about both, and that Eph 5 is a precedent for arguing this way. According to your view, the Song cannot be about human marriage. But I would say that the typology also works in reverse. If it is about God and His relationship to His church, then it is also about marriage, since the two are organically related (again, see Eph 5).
Given my understanding of the function of a type I find this way of speaking quite confusing. One may not argue from the Antitype back to the type. It is like reversing history. The book of Hebrews makes it abundantly clear that the type gives way to the Antitype; if it were otherwise, the Hebrews would have been quite justified in continuing with OT ceremonies. Earthly marriage shall give way to the eschatological marriage. It may even be argued that the "first" marriage alone is a type because it is distinguished by the characteristic of being without spot, a characteristic which is not to be seen in post-fall marriage. There are also numerous ways in which it is fallacious to argue back from Antitype to type with regard to marriage. E.g., there is legitimate divorce, and there is the reality of death breaking the bond. I am sorry, but the acceptance of your third point would turn the reformed understanding of marriage on its head.
Fourthly, your argument from the canon doesn't work either. It doesn't have to have New Testament attestation as being about marriage if it echoes the Garden of Eden. I don't really have time right now to explore that, but I would say that being naked and unashamed is an echo of Eden, and the descriptions of the man and the woman of each other follow that line. The references to the garden paradise (even down to the possible Persian loanword) also point in this direction.
As noted above, the characteristic of being without spot is not possible after the fall, and will not be seen again except in the eschatological bride of Christ. The garden imagery is legitimate and I accept its functionality within the Song; but this provides an argument against seeing human marriage as the reference point.
My argument with respect to the Canon is an important one. On what basis do we accept this book as canonical? The numerous allusions in the NT would place it on an equal footing with other books which are directly referenced with a Christocentric message.
Fifthly, your assertion that the descriptions of the man and the woman are "ghastly" if referring to human love don't work, because you are stating that objection from a Western perspective. The descriptions I have read of the point of the metaphors as descriptions of human beauty are anything but ghastly. You should test your assertion against some of the modern commentaries, which are becoming more and more adept at seeing the point of the comparisons as being a thing of beauty, and not of ghastliness.
No, I stated that would be the case even from an eastern perspective. The examples of love poetry from other ANE cultures demonstrate that physical beauty was expressed in terms of other earthly objects which were pleasing to the eye. It is accepted by scholars who have compared these with the Song that they are of a different nature. The imagery in the Song does not present the physical appearance in terms of objects of desire and pleasure which are of an earthly nature. They are more abstract; in fact, they are religious by nature. There is sensuality, but the senses are informed by religious teaching. This provides another argument in favour of the strictly allegorical approach.
Since you mention modern commentators, I will take this opportunity to voice my objections to the "love song anthology" view.
(1.) The concept of an anthology contradicts the title of the Song, and requires a strong subjective bias to determine the structure.
(2.) On this view "Solomon" must be reinterpreted in a non-historical way and denied authorship in some sense. Once internal textual controls like this are rejected there is really no way of hoping to arrive at the author's intended meaning.
(3.) The characters are non literal. They are fictional. This means that they function in the abstract in the same manner as an allegory. The road by which scholars have come to the point of identifying genre as "love poetry" is by rejecting the concept of allegory. If they are going to accept abstract terms of reference for the words of the text then they are genuinely required to explain why the original approach was invalid in the first place. It is worthwhile observing that this "generation-gap" in biblical introduction is apparent in most modern works. An earlier generation has rejected one reading and posited a new reading, while a subsequent generation rejects the preceding reading without considering the earlier rejection of an original reading. Such a trend can only spiral downwards.
(4.) There is no "marriage" in the book. At best, those who follow Childs' canonical process approach can read marriage into the story from the broader canonical requirements for sexual intimacy. Those who do not take this approach are able to look at the book's internal features and conclude that the kind of sexual intimacy is in fact anti-institutional; the fictional characters of the book are then able to be understood as representing "institutional love" in some way. From my point of view, they would have a strong argument because they are reading the book as an integral unity and are not forcing concepts from other literary environments. Also, the "presupposition of canon" undermines the process by which we acknowledge the internal marks of Scripture and accept a book as canonical. Without this process we have no basis upon which to reject a different canon. Why is the Song in the Protestant canon of Scripture? It was accepted on the basis of its allegorical nature and because it did not speak of human love. Those who insist that it speaks of human love are therefore bound to explain why it should be regarded as canonical, at least within a Protestant context.
(5.) If we cannot find "marriage" in the book, how can it be regarded as holding forth ideal human love? Ideal human love is God-united love. The absence of God in even a fictional capacity in the book means that there can be nothing "ideal" in the book. Further, if there is no marriage in the book, the issue of moral questionability comes to be raised of the "love poetry" reading as equally as of the "drama," "typological," and "literal" readings.
(6.) If the symbols of the book refer to human love of an idealised nature, the book as a whole must be leading us (1) to think of marriage as ideal, and (2) to seek ideal marriage. As already noted, the "ideal" of marriage is to be found in its divine institution. This institution left open the option not to enter into marriage for higher purposes. It also made provisions for the function of marriage under the fall. In fact, under the economy of redemption, "love" takes on new characteristics relative to its less than ideal situation; self-sacrifice rather than physical indulgence becomes the emphatic requirement for marriage in the fallen state. If the Song intended to teach about human love in an idealised form it becomes an unrealistic book in a fallen world, and would be irrelevant for those who are not married. In fact, it might serve as a temptation for those who are unmarried, especially when they see the exaltation of physical pleasure without any respect to divine institution.
(7.) Finally, the doctrine of the soul-body unity which is being advanced in Tremper Longman's NICOT commentary is highly questionable from a reformed point of view. He doesn't give a detailed explanation of his terms, but he says enough to show that this approach to the Song is perhaps being guided (or misguided) by erroneous views of human sexuality. To what degree these views affect the interpretation of the book is difficult to tell; it may be that the love poetry reading can exist without these views. Nevertheless, there is something in these erroneous conceptions which makes the love poetry view to be more appealing, and that should at least make us stop and examine ourselves before we enter into the presence of the holy and take up holy things lest we do so with unclean hands.