There is not really much you can do to fix the multiplayer bug in TPR unless you're an extremely skilled ASM hacker (and even then it would be difficult considering that the real problem isn't known). In the original game the saving pretty much works so if you can install the game from your old CD then you will be able to play multiplayer.
Is there IPX multiplayer option in KaM? I never noticed that and always thought IPX was DOS only but seems like I have been proven wrong. I sometimes also get problems with the box popping up, but with some reboots it will eventually appear.
Using the compability mode under WinXP when playing KaM (at least TSK) actually breaks the game, yes B-R-E-A-K-S it. At least for me the game instantly crashes if I enable the compability mode and try to run it. I haven't tested it on other versions than 1.32 though, so it could work on 1.20, 1.30 or 1.31...
EDIT:
Forgot another thing, there's also another bug in the multiplayer in TPR that causes the game to desync after playing for some while. If you're playing on a LAN there shouldn't be any problems as your ping should be low, but when playing online it is extremely annyoing, which is why I stick to TSK in multiplayer.