Thanks again for your helpful suggestions. Just to close the loop in this in case anyone else has trouble and sees this thread:
For some reason, I was never able to use copy/paste to transfer my iTunes files from my USB-connected drive on my iMac to the Synology NAS. All of the folders were duplicated, but not the files. Very strange. I also tried the same thing using the file transfer utility built into the NAS, with the same result. Folders other than iTunes transferred just fine using copy/paste, by the way.
On a whim, I tried drag and drop from the finder, and that did the trick. Everything copied over just fine. I have no idea why this worked when copy/paste did not, but in the end I got it done. Once the files were copied to the NAS, I started the Apple music application on my new Macbook Pro, set the iTunes music location in preferences to the NAS, and all of my playlists and files were there with no problem.
The Apple TV app was a bit more problematic, since it did not find my video files even though I set the preferences to the right folder. Instead I had to import each one, and re-download the artwork.
All this took a few hours, but eventually I got it all up and working properly. I watched iTune devolve over the years into what I consider a bit of a mess. iTunes Match, home sharing, family sharing, etc. all seem to operate under different rules, and not well. I realize that the world has moved more to a streaming model and that supports Apple's future plans, but it doesn't quit work for me. The next time I have to do this, it may be time to move to something better supported, or at least less proprietary. Apple support was absolutely no help since the fact that I was using an NAS let them off the hook for any responsibility in their view. The volunteers on this board are pretty helpful though, so thanks for that again.
Don