It seems that you're using an outdated browser. Some things may not work as they should (or don't work at all).
We suggest you upgrade newer and better browser like: Chrome, Firefox, Internet Explorer or Opera

So playing a little bit of Warcraft II, and it isn't quite the way I remember. Most notably, the music. I recall the music playing just one track continually per stage, but now it keeps cycling through tracks ever couple minutes. I also recall there being an option to play midi music instead of the CD audio so you can have it loop seamlessly.

Maybe it's because this is the Battle.Net edition instead of the original version. I still have my discs for the original version, but they don't play on my modern machine. Hell, they don't even play on some of my old WinXP computers.
Is there some way I can fix these issues, or maybe get my original versions to play? Can I possibly replace the files in my GOG version to use the original?

It's great to be able to play this classic again, but I want to get the experience right.
I'm in the similar situation, since I prefer the DOS version, especially that SB16 music sound. Therefore I have both the BNE and the original, which I've configured via DOSBox on Win7. If you google "DOSBox Warcraft II" you'll find some guides that will help you set the game to work on newer machines. You'll need to make an image out of the game's CD. Let me know if you need further guidance, I'll try my best to help with the setup.
For AudioCD issue - it cause you play old DOS version on same machine - with Windows 7. Some "security" features disable AudioCD support and now in any later OS Windows - only 1 track per loading are work from CD.
you could use dosbox to get the original version to install and run.