In other words, when you sing Psalm 72, what you are really singing in your heart is "Jesus shall reign where'er the sun, doth his successive journeys run..." You can't have it both ways. Either you are stuck in the types and shadows (glorious as they are) or you are really singing in your heart a New Covenant exposition of the psalms (your "man made" application of the psalm to Christ - note "man-made" does not mean wrong, or sermons would be ruled out). Which is what we do when we sing a hymn....
I freely admit that I am singing with a New Covenant understanding. As Paul says, we sing with understanding. The Psalms have only have one meaning, and the New Covenant meaning is the meaning. It's not a secondary layer of interpretation, but the primary point. Just the same as I read the works of other prophets in the Bible in a New Covenant understanding without seeing any need to supersede or alter even one jot and tittle of any of it. And I go so far as to say, if one cannot understand Christ as He is in the Psalms, there will always have a deficient understanding of Christ, whatever else you understand from the New Testament. The disciples spent three years with Christ, saw far more and learned much more than we ever read in the Gospels, a world of books like John says, yet they did not get Christ until the Psalms (with the Law and Prophets) were opened to them. Their minds weren't opened just to see that Christ was in them, but to know Christ
from them.
Luke 24:45–48 (KJV 1900):
Then opened he their understanding, that they might understand the scriptures, And said unto them, Thus it is written, and thus it behoved Christ to suffer, and to rise from the dead the third day: And that repentance and remission of sins should be preached in his name among all nations, beginning at Jerusalem. And ye are witnesses of these things.
Until the Old Testament was unlocked, there could be no power at Pentecost. The Psalms were the sharp arrows of Christ to pierce the heart of those who fought against Him (Ps 45). They did not need updated Psalms or songs--they needed to understand what the Psalms and prophets were truly about. And the people saw Christ so plainly from the opening of Psalm 16 and Psalm 110 (along with Joel 2) by Peter that 3000 were pierced, repentant, and baptized. What steadied the minds of the apostles when the Jewish leadership began to rage? Psalm 2. What kept eyes of the Hebrew Christians in Rome on Christ? In the fist two chapters of Hebrews, the author uses Psalm 2, 8, 18 (possibly), 22, 45, 102, 110. The use of the Psalms only steepens as you get through the Hebrews. Old Covenant era songs were New Covenant weapons.
Brother I know you understand these things. My point is that the Psalms as written were perfectly sufficient for the NT church to reveal Christ, and were indispensable to know Him in those times. And if indispensable, then Christ can be as plainly known from the Psalms as in the New Testament, evidenced by the fact that they were such a powerful weapon to convert and edify.
So I say, the Psalms are New Covenant songs.
It's not me alone, but one only need to pull out Spurgeon's "The Treasury of David" or Matthew Henry's commentary, read on the psalms I mentioned in the post you quoted, and they will never again fail to see Christ as clearly in those psalms as they see Christ in the New Testament, and in ways they never thought possible. In fact they will say, "How did I ever miss it?" At first we don't recognize Him. Like at the tomb, we are certain that they are the voice of the gardener that has laid Christ in a hidden place; then Christ shows Himself to the understanding, and in amazement and wonder we say, "Rabboni! Master!" Then we say, "Didn't our hearts burn within us as we read and sang them?" And again in the words of Thomas, "My Lord and my God!"
Minor Edit @ 8:20 AM