The roots come from the actual command to worship with music using musical instruments.
Psalm 33:2-3
Let the godly sing for joy to the Lord;
it is fitting for the pure to praise him.
2 Praise the Lord with melodies on the lyre;
make music for him on the ten-stringed harp.
3 Sing a new song of praise to him;
play skillfully on the harp, and sing with joy.
Psalm 150
1 Praise the Lord!
Praise God in his sanctuary;
praise him in his mighty heaven!
2 Praise him for his mighty works;
praise his unequaled greatness!
3 Praise him with a blast of the ram’s horn;
praise him with the lyre and harp!
4 Praise him with the tambourine and dancing;
praise him with strings and flutes!
5 Praise him with a clash of cymbals;
praise him with loud clanging cymbals.
6 Let everything that breathes sing praises to the Lord!
Has God somehow changed His mind? Hardly.
Colossians 3:16
Let the message about Christ, in all its richness, fill your lives. Teach and counsel each other with all the wisdom he gives. Sing psalms and hymns and spiritual songs to God with thankful hearts.
The Greek "psalmos" consistently means "a song of praise with an instrument", and therefore renders the argument of no instruments as invalid. What is valid is to use all available instrumentation to bring praise and worship to our Lord. If a group doesn't want to, that is their choice, but to declare the full array of instrumentation available to glorify God as somehow evil or wrong, is extreme, to say the very least. IMHO, people who do not exalt the Lord using musical instruments for the reasons given in this thread are missing out on the great blessing that comes from worshiping fully, and also hindering people who have a skill in playing an instrument from enjoying the Lord and blessing Him.
Again, every scripture you quote here is from an old dispensation, when the Holy Spirit was not indwelling God's people and they were unable to worship in spirit and in truth in the way that we are able to.
You ask if God has changed His mind. I wouldn't say that, but I would say that He changes His relationship with man according to His eternal purposes. 2 Corinthians 3 is one of the chapters which sets out the way that His purpose has changed between the time which the Psalms refer to, and the time Colossians refers to.
And isn't the contrast between Psalms and Colossians plain? One speaks about a great variety of musical instruments employed in praise. The other speaks about psalms and hymns and spiritual songs sung from the heart. Every reference to musical worship in the New Testament refers to singing, and often mentions the heart and / or the spirit. A striking contrast to the Old Testament.
A radical interpretation of one or two Greek words has no weight whatsoever when we consider that musical instruments were never used in association with Christian worship for the first 600 years of the Christian era. Even if the silence of scripture holds no sway with us, perhaps the silence of history does.
What is most disturbing about all this is the suggestion that a believer or gathering of believers cannot possibly worship God fully without the addition of props, whether its musical instruments or whatever else. The typical teaching of the offerings of the Old Testament clearly shows the error of that. The unmixed character of many of the offerings show them to be purely of Christ, without any addition. That is what the believer offers to God - Christ, without any admixture or addition required. If we understand these typical teachings it should really give us a deeper and fuller sense of Jesus as the only acceptable offering - for sins, yes, but also for the pleasure of God now and eternally. As I've said before, we can't possibly add Adam to Christ in order to please God. Cain's offering simply can't come into the equation.