And if your singing does not offend Jews? Here we see one of the key differences between us. Where does singing fit as an element of worship? Is it more like preaching and praying or like reading Scripture? By the way, 2 Tim 3:16 and 4:2 undoubtedly refer to the OT Scriptures in their original context, so don't give you the warrant you need.
Every element stands or falls on its own, so asking which it is more similar to is a moot point. Every element is regulated on its own. Preaching something outside of the explicit words of scripture is not optional, it is a command. Praying our own words and composing our own prayers is a command. We have a command to read scripture. We have a command to sing psalms. Where is the command to compose new songs?
Undoubtedly they immediately refer to the OT scriptures, but do they not give warrant for NT preaching as well? Or do you think that preaching NT texts is a mere human ordinance and not of divine command?