Update on this. The extended review by Matthew Winzer should be out along with the rest of CPJ 4 in early December. It is slated to complete next week by the 26th at the book maker, and then it is simply a matter of it getting the freight here and then getting issues out to the subscribers. Matthew did some fine work.
The review opens thus:
An attempt has recently been made by Nick Needham “to give an accurate historical judgment relating to the [Westminster] Assembly’s views and deliverances relating to exclusive psalmody and non-instrumental worship.”1 If, however, one were expecting to find a detailed examination of the writings of the divines, he would be sorely disappointed. Throughout the article reference is made to only one fragment of writing from a member of the Assembly; all other quotations are taken from the statements of individual Puritans who neither attended the Westminster Assembly nor spoke specifically to the issue of exclusive psalmody. Moreover, no use has been made of the valuable historical material to be found in the writings of those members who have provided some sketches of its proceedings. Given this regrettable state of affairs, it must be said that the article fails in its attempt to provide an accurate historical judgment on the Assembly’s views. Whoever is the rightful possessor of the views Mr. Needham has represented, they have not been shown to belong to the Westminster Assembly.
1. J. Ligon Duncan, The Westminster Confession into the 21st century, 2, ed. J. Ligon Duncan (Ross-shire, Scotland: Christian Focus Publications, 2005) xiii. Hereafter referred to as Westminster.
Matthew then proceeds with reviewing Needham's handling of the regulative principle, singing of psalms, and then briefly, musical instruments. The most extensive section is the middle dealing with Westminster and singing of psalms. Under that portion of the review he covers.
- The Historical-contextual Interpretation of “Singing of Psalms” in the Westminster formularies.
- External Evidence: the Milieu of 1640s London.
- Advocates for Exclusive Psalmody Amongst the Westminster Assembly of Divines.
- The Wider Puritan Tradition.
For those interested in the subject this review is practically worth the price of the issue.

And you get much more with it.
Marty,
There is a relatively short review in CPJ 3 within the second part of the survey of sixty years of regulative principle material, and my appendix to it bouncing off of the Needham is posted on my PB blog. Matthew Winzer, who did the leg work for the few pages in CPJ 3, is working on an extended review of Needham's work for CPJ 4, D.V.
The Meaning of "Psalm" in the Westminster Standards - The PuritanBoard