Oh. My. God. I just had to add the CD Audio drivers from the Win setup disks. Thanks! Wow. This is great!

If you want to play CD audio in Windows 3.x then you need to install the CD Audio driver:
http://www.findpk.com/cybercity/WIN3X.htm

Just wanted to post some of my experiences here so someone isn't trying to recreate the wheel if they attempt to install this game in Win 3.1x.

- Obviously, the [MCI] CD Audio Drivers need to be added if you want music in the game. Not sure how I missed that in my original install of Civ2 and 3.11.

- Sometimes if you install the English version of the game, there will be only Greek-ish looking text in the menus. This is due to the default Civ2 font missing from your installed fonts and the system defaulting to 'symbol'. This can be remedied by going into the Control Panel and adding all the fonts if you're impatient like me, or attempting to isolate them by adding them one by one.

- There are multiple hangs I've found that were remedied by using the 2.42 patch from the great folks over at CivFanatics. Mine would hang every time a tech was discovered (the screen loading still takes a bit of time and I haven't tested it repeatedly). Make sure you call the 'c:\mps\civ2\civ2.exe version of the game in your launch command conf file in DosBox as opposed to the d:\civ2\civ2.exe version as it will still be v1.00 (checked by pressing ctrl+o in game).

- I am still unable to get this to launch when using runexit.exe (most updated version 2013, IIRC).

This install was done on a clean Win 3.11 installation using the guide from this here wonderful forum. Hope this helps someone in the future and thanks to Jorpho for sticking with me through some pretty embarrassing learning experiences. Glad I'm able to preserve this (massive) part of my childhood.