tl;dr: V20 soundtrack doesn't appear to work. V17 is working (hey, we're back where we started :^) ), V2 of soundtrack, and music changer. My soundtrack should be the same as the one in the mediafire link since that's where I originally downloaded it from.
Alright, so... I think you're right in your assessment that V20 doesn't have the soundtrack working (and I'm guessing the fact the culture system was reworked in V20 has something to do with it).
Admittedly, it was/is a pain in the ass to verify whether the soundtrack is actually being applied. There's probably an easier way but I was just trying to do a quick test and ended up just using the music changer mod and hopping into a V20 cultural diversity modded game with everything enabled.
Halfway through I wondered if the soundtrack was ever working to begin with and if I was experienced a version of the mandela effect I swore that I heard songs that were noticeably different from the civ 5 ones. I spent a large amount of time on V17 but only a few games on V20 so it was possible for me to be remembering V17 all along. After listening to the vanilla songs for comparison and spamming the music change button with Portugal and Mongolia I'm going to say that V20 doesn't work with either V2 or V3 of the soundtrack (tested just to be sure since I used V2 a lot more).
Good news is that V17 does work (you can tell the song is probably added in if it incorporates vocals. With Mongolia, you're going to get some Mongolian throat singing and women singing, for example. I tested out V2 of the soundtrack (old one available on mediafire) so it should be working on your end. Easy way to test is to select Mongolia and listen for Faun, Huun-Huur-Tu, or Turkic5 songs.
Bad news is that I am not currently playing civ 5 so I don't want to spend time trying to investigate V20's problem with the soundtrack, which would probably explain why the soundtrack download was removed :^).
I tried using v18 but still no.
How did u manage get it working?