I think I had luck with starting RTST / PS2 first. Having OBS running but not capturing, then in-game with our overlay displayed start the capture through a hotkey. I believe this worked in full-screen with game mode capture. However alt-tabbing / changing graphics settings broke it completely.

There really isn't a way to force the order after that unfortunately. OBS game capture uses a hook like we do and if its hooked before us it won't see what we render.

The streaming overlay wouldn't have an issue with it though.