If map scripts cause an OoS on turn 1, you can save and then load that savegame and it should work.
Whenever I got OoS reports I have tried to fix them so they should be quite rare now. Important is that there are some BUG options that are unsynced and need to be set to the same on both computers.
We did restart the game, like you suggested, multiple times. Still constantly getting OoS error every 3 turns. However we do have many features on(revolutions, assimilation, random events etc.) and maybe they are the cause?
Going to double check BUG settings on both just in case if there is some variable unsynched.
Glad to hear if most of the problems are truly solved already. Guess it is just a taste then what you pick up as your settings for the game.