I have never been able to finish a game on Mole Shopper because of desync, whether it's when I host or HostingBuddy hosts. What's going on? A bug that needs to be fixed.

I'm not a coder, but desync seems fixable. Why can't the person who is out of sync, sync back to whoever's turn it is? For a turn based game, this really shouldn't happen...

I do have ProjectX installed, may that be the problem? Does it happen with you guys?

ProjectX causes many troubles, one of them is desync from online games. Im not saying it has to be PX in this case, but i suggest you to get rid of this.

I think I have same problem. (espercially non-PX games with HostingBuddy)
Try uninstall Project X.

Remove Wormkit modules until the problem is resolved, let us know if you do or don't use Wormkit. A quick way to test is to run the game via wa.exe instead of Wormkit.exe and play a few games.