I just played the Random Huge (Multi) map with two friends on a LAN (all three of us allied). We discovered that two of us - Coridane and Orion - were in sync (in the same game) while the third - Kyonu - was not. He seemed to be in his own game. I believe we could chat with him and send him credits and mats (not sure on that), but I know that I sent him a trade pact, and he never received it. I remember him seeing different bounties than what I saw. I would also see planets that he controlled as enemy controlled. The most conclusive evidence of this bug though was when we were in the same gravity well, but seeing different things. In a saved game that I can send, orbiting Alpheratz (the far right star) is Ganesa. Orion could see his Titan engaging a Rapture. Kyonu did not see that. He saw an enemy starbase, a novalith cannon, and a huge fleet. I could see what Orion saw. A minute or two after the save, I sent my forces through a wormhole that connected to Ganesa, jumped to Ganesa, and offered support to Orion. Kyonu could not see me and we could not see Kyonu.
I don't know if the save will really help you, but at the very least, it shows you what two of us were seeing. We should have had Kyonu save. Does only the host auto save? Orion was the host.
Before this game, we were playing a game that crashed, so that may be related. I have the dump file if you want it also.