I've heard Mupen64k is better than Project64k but that's about it

(Not sure how different they are tbh...)
Personally, I think they're both kinda.. crappy. You're better off just not using LAN at all - Kaillera is terrible, and most multiplayer implementations for N64 are pretty bad too. (Not sure about Mupen64k because I've never tried it and the source code was lost)
If you still wish to, then you can try. It's unlikely you'll get anywhere, but under a LAN you might at least be able to keep sync. Under LAN you should directly connect computers in the multiplayer mode instead of going to an internet server.