An anonymous commenter provided essentially five interrelated criticisms of Psalmody, which are produced (with added numbering and italic face) below. My response is in plain face.
1. "Recall what Jesus told James and John when they wanted to call down fire from heaven like Elijah? "Ye know not what manner of spirit ye are of. For the Son of man is not come to destroy men's lives, but to save them." I think he would say the same to those singing most of the Psalms, seeing they call for vengeance against enemies and beating them small as the dust and so on."
Respectfully, I'm not sure how familiar the commenter is with the Psalms. Surely there are some Psalms that call for God's victory over his enemies. Likewise, I think that the commenter is assuming that Christ's ministry brought a shift rather than a fuller revelation of what was already known by faith in Old Testament times. The Psalms are balanced, and divinely so.
2. "Not only that, but the Psalms also speak of animal sacrifice as still accepted by God (because it was when they were written).
I haven't done an exhaustive survey, but surely the Psalms mention animal sacrifices, but also mention their insufficiency, for example:
Psalm 40:6 Sacrifice and offering thou didst not desire; mine ears hast thou opened: burnt offering and sin offering hast thou not required.
a) "Not only that, but Paul says that Christians are to speak the gospel boldly, "not as Moses, which put a veil over his fac[e]" and does that not also apply to singing?"
2 Corinthians 3:12-15
12Seeing then that we have such hope, we use great plainness of speech: 13And not as Moses, which put a vail over his face, that the children of Israel could not stedfastly look to the end of that which is abolished: 14But their minds were blinded: for until this day remaineth the same vail untaken away in the reading of the old testament; which vail is done away in Christ. 15But even unto this day, when Moses is read, the vail is upon their heart.
This argument is actually interesting, and it is the first time I've heard it made. Still, the way that we can readily take away that veil is by - in addition to the singing - read from and preach the New Testament.
God could have inspired a new or expanded Psalter, but he did not. Furthermore, in many cases the Psalms speak the Gospel more clearly than the Law does.
b) "Should we sing in shadows and figures or in reality?"
Well, when we sing Psalm 23's "The Lord is my Shepherd," we certainly know that this psalm speaks of the Lord Jesus Christ. We may not use the name Jesus, but from the remainder of the sermon, the type does testify to the antetype.
4. "I have seen also a very good argument against exclusive Psalmody based on Col 3:16, "Let the word of Christ dwell in you richly in all wisdom; teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord." in which it is asked if perhaps it should be read thus "Let the word of Christ dwell in you richly, in all wisdom teaching and admonishing..." Isn't he commanding them to use their wisdom to compose songs that can teach the message of the gospel?"
That's a very orginal argument, but I wouldn't call it strong.
As you should be aware, there is a parallel instruction in Ephesisans:
Ephesians 5:19 Speaking to yourselves in psalms and hymns and spiritual songs, singing and making melody in your heart to the Lord;
That passage would be more helpful to this particular argument in some ways, because the parallelism in Colossians 3:16 is between "Let the word of Christ dwell in you richly in all wisdom;" on the one hand and "teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord." One might even argue that the verse has been incorrectly punctuated, but we need not reach that issue, because no one would suggest that "word of Christ" is something that we compose, as compared with Scripture.
It's interesting to note that the parallel includes the "wisdom" component, but also includes another component that is perhaps unexpected:
17Wherefore be ye not unwise, but understanding what the will of the Lord is. 18And be not drunk with wine, wherein is excess; but be filled with the Spirit; 19Speaking to yourselves in psalms and hymns and spiritual songs, singing and making melody in your heart to the Lord; 20Giving thanks always for all things unto God and the Father in the name of our Lord Jesus Christ; 21Submitting yourselves one to another in the fear of God. 22Wives, submit yourselves unto your own husbands, as unto the Lord. 23For the husband is the head of the wife, even as Christ is the head of the church: and he is the saviour of the body. 24Therefore as the church is subject unto Christ, so let the wives be to their own husbands in every thing. 25Husbands, love your wives, even as Christ also loved the church, and gave himself for it;
16Let the word of Christ dwell in you richly in all wisdom; teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord. 17And whatsoever ye do in word or deed, do all in the name of the Lord Jesus, giving thanks to God and the Father by him. 18Wives, submit yourselves unto your own husbands, as it is fit in the Lord. 19Husbands, love your wives, and be not bitter against them.
What are the parallels:
1. Be wise;
2. Sing the Psalter (its historic divisions were the Psalms, Hymns, and Spiritual Songs, as Michael Bushell adequately proved in Songs of Zion) as your way of exhorting one another;
3. Give thanks to God in prayer through Christ's mediation;
4. Wives submit to their husbands; and
5. Husbands love their wives.
When you look at the parallels, the point of the passage almost immediately pops out! It's a recipe for Christian unity. How can we argue when we are singing the Psalms? How can we seek the preeminence we acknowledge one mediator betweeen God and man? Surely, there is some hierarchy (after all, wives submit to their husbands - which lends itself to peace as well), but there is also to be charity (for husbands are to love their wives - which also lends itself to peace).
In short, the passage is a recipe for peace. And look at the preceding context in each case:
Ephesians 5:1-2 & and 15-16
1Be ye therefore followers of God, as dear children; 2And walk in love, as Christ also hath loved us, and hath given himself for us an offering and a sacrifice to God for a sweetsmelling savour. ...
15See then that ye walk circumspectly, not as fools, but as wise, 16Redeeming the time, because the days are evil.
12Put on therefore, as the elect of God, holy and beloved, bowels of mercies, kindness, humbleness of mind, meekness, longsuffering; 13Forbearing one another, and forgiving one another, if any man have a quarrel against any: even as Christ forgave you, so also do ye. 14And above all these things put on charity, which is the bond of perfectness. 15And let the peace of God rule in your hearts, to the which also ye are called in one body; and be ye thankful.
So, that ought to make it clear that the point of the passages is that we should join in the fellowship of unified Psalm-singing corporate prayer and mutual submission/love, rather than ceaseless strivings and contentions.
There is a place for debate, but there is more to life than debate.