Good question! To really understand the issue, and to answer your query, I believe that an indepth study of Church History (especially Restoration History) would be in order...
My understanding, based upon Restoration History (that is the facet that I will deal with, at this point), is that the issue became one of major debate toward the end of the 19th century. Until then, church autonomy prevailed in such matters... That is, until M.C. Kurfees, and others, hit the scene.
Up to this point, the music question was of somewhat concern in the RM brotherhood, but was not an issue of "fellowship", nor an issue of "essentiality". Kurfees, it seems, changed this perception, and began to preach that this "presumptious interference with the divinely appointed worship"... this "high handed sin"... was one that needed to be dealt with and opposed. It was indeed, to him and to those that followed after him, a matter over which one's salvation was assuredly dependent. He used the verses you mentioned in establishing that there is a "pattern" for worship, and that it is "divinely appointed". To add instruments in our worship to God, would be to "go beyond the things which are written."
His impact, along with the impact of others, divided the RM, as I'm sure that you well know. From one Movement begun to unite all Christians in all denominations, sprung three sects identifying themselves as "Disciples of Christ", "The Church of Christ", and "The Christain Church".
M.C. Kurfees, along with others, have used these verses to try and prove their point... This is called Biblical "Scholasticism". It is the practice of searching the Scriptures to prove one's current practice or understanding. Such a practice usually ignores the context, both immediate, and otherwise.
As you have already stated, the immediate context, in the case of these two verses, does not merit such an interpretation... In fact, the verses in and of themselves, drawn out from the context, do not even merit such an interpretation... Unless one is looking for it.
I could say much more on this issue, but will refrain for now. I will wait and see what others have to say, first...
By the way, I have, in the past, preached like Kurfees preached... I have been down that road. But, like all roads, they eventually lead you somewhere. After arriving, many times you realize that, although you have travelled a long way, you ended have up in the wrong place. In such a situation, one can be content with being in the wrong place, given that the travel took so long... But one can also get back on the road, and continue his travel, until he arrives at the right destination...
"Search the scriptures; for in them ye think ye have eternal life: and they are they which testify of me." (John 5:39)