Oh, so it's not as simple as one issue and requires avoiding bunch of caveats and a lot of MP testing.
This is troubling, as obviously I don't play factorio multiplayer at all and can't really do the latter, while changing a lot of things is also somewhat difficult as I don't have much spare time to dedicate to this atm.
So guess I'll have to put up a notice that mod is not compatible with multiplayer in general and leave it at that.
If you or anyone else can find and fix/test places where multiplayer issues occur, shouldn't be a problem to merge these fixes into the mod, but don't think I can do it myself.
Thanks again for looking into this, and sorry if it caused you a bit of pain and work, didn't know it was that tricky to have factorio lua stuff to work in multiplayer.