We're getting ever closer, but not close enough:
1) I tried using both wine version 2.0 and 2.21. No luck.
2) Installed the component "DirectPlay" to my Heroes3 in PlayOnMac. Bingo! Now when I host a game, I end up in the multiplayer lobby, which means we're one step closer.
Now the problem is that none of us can connect to each other, even though we can see the hosted game in the list.
3) Tried to connect using our real IPs, and not the ones provided in the game. No luck.
4) Gave up on TCP/IP, and went for GameRanger in stead.
Turns out my Mac version of GameRanger can't regognize my windows version of the game.
5) Tried installing GameRanger in PlayOnMac. Wouldn't install.
6) Installed components "flashplayer", "mfc40" and "mfc42". Bingo! GameRanger now installs.
....then it crashes.
7) Switched from wine version 2.21 to 2.0 (thanks for the tip). Installed GameRanger again, with components flashplayer, mfc40 and mfc42.
GameRanger is now stable.
8) Tried to host or join game through gameranger. Windows version of GameRanger now recognizes my game.
Crashes upon launch. I'm guessing that's because GameRanger can't run the game through Wine/PlayOnMac.
9) Now given up on the whole GameRanger mess. Going back to trying to get TCP/IP to work, as we felt we were closer there.
Any suggestions?