Brother, I am honestly beginning to believe we may be have a cultural or contextual misunderstanding - and I certainly apologize if it is so!The point is, good fellow, that you can't read, pray AND sing the Psalms all in one motion, as is clear from the very manner in which you state the case. The Bible clearly distinguishes these actions as modes of worship. The sooner you concede the obvious, the sooner this discussion can proceed apace.
I can certainly read, pray and sing a Psalm simultaneously - unless you mean read in a declamatory fashion as opposed to read the text on the score and pray the words as I sing them. Which I do quite often, BTW...
By day the LORD commands his steadfast love,and at night his song is with me,a prayer to the God of my life.