I have determined the exact option that's causing the error. It's... "Use Alternative Start Sequence"? I am in awe something so innocent-looking could be the problem.

Edit: I played around with the function "AlternativeStartSequence()" in the mods's gamemain.lua. Emptying the function does not fix the problem. Replacing it with the contents of the else statement—the line 84 in particular—did, however. The rest is beyond me, unfortunately. I do not understand why recursively calling OnFirstUpdate(), which seems to call UIP.OnFirstUpdate() every time, results in the replay working properly. I checked that function, and it's completely empty.

Edit 2: And it has to keep calling itself in particular. Making UIP.OnFirstUpdate() call itself in its own function in UI-Party.lua does not fix the problem.

Edit 3: The only fix I can imagine is a workaround, and it's to add a check for if the session is a replay and not trigger the alt start if that's the case. This made me think; if you could also switch between players during a regular match, would this problem appear also? I launched a quick game alone, and no, this does not seem to be the case. The rarely repeating errors that seem to be the prelude to the lag once you flip from player to observer seem to be absent, also.