I have the same problem, it happened to me while playing single with 4 AI (1 destroyed), I'm just stuck at turn 233. Happened to me before, but with 6 AI at turn 72. Kind of sucks, since I was near the end of the game. Also, the first save is on cloud, while the seconds is "normal". Maybe it's a problem with longer and more complex games, having their "memory capacity" (because of the Empire Chronicles or something like that), if that's even a thing, just taken or something?

You get bump from me as I get the same issue, 2 human players, I am the host.

I first thought maybe it was some access violation, closed all 3:d party programs, basically loading windows barebone.
Issue still persisted.

Our first game was against 8 AI's: It first started to happen around turn 12 i think. and kept getting worse after that (Although a few turns did go smoothly).
Where the ai would take 1-8 minutes after me and my MP friend had pressed End turn to actually finish (so not counting the time before).
I observed that always when this happens, the whole turn not up until it ended. Not even the players ships moved until the turn ACTUALLY ends.
Pressing the "move all ships" didnt do anything until then basically. Which was annoying if you wanted to actually scout anomalies (We had in this game a 180sec turn timer ... so could not always do this)

After almost 2 hours, we had only got to turn 20 or 21 when it compleatly froze up. After 10 min (after a reload too) we gave up and hosted a new game last night. 

This time with 6 AI ... Same issue at turn 6 sadly... I didnt have the patience or time to wait myself so just called it there :(. (120 turn timer)

PLEASE look this up and let us know if there is a workaround! <3 I love this game but its hard to like it and reccomend it to more friends when you cant even start a basic multiplayer game you know :P

I will here include my DXdiag, diagnostic files, Autosaves and dumpfiles i believe will be relevant for you Devs!

P.s. If you prefer the files one by one over a zip file, let me know

Endless space 2 bug.zip

Also a side note. At one occation we tried a manual save to see if we could get around this by reloading. This somehow forced the AI to end their turn and it "locked" itself up and we could just continue from there over a reload.

However the second and third time we tried this, the game basically locked itself up and it got stuck during saving (with the end turn icon having the "saving in process" animation forever forcing me to force close the game with ctrl shift delete.

I also suspect this dose not belong here? Maybe a mod would be so kind to move this to the bug report part of the forum ^^