Update for you Frag:
When this occurs you can cancel or "deactivate quantum gateway" on the gateway it spawns at (even if that one is an enemy's), but then weirdness occurs. It will deactivate their quantum gateway (or maybe in code land it's now "yours"?) but not delete the gateway. Leaving a permanent gateway there. Preventing any new ones to spawn, etc. etc. - You may need to make a nuke gateway big red button function at some point just to clear & reset.
It's hard to narrow down an exact rule set on when/how exactly it starts choosing other gateway(s) besides where the fleet is located. My initial thoughts were off. So far the constants are multiple gateways (obviously) and there is open borders between my Gateway and theirs (whether through war or diplomacy) - but haven't 100% tested that last one as required. Order of initial completion of gateways is not it - I've been second before and still lose out eventually. Maybe second/third to activate gateway? (you fire/cancel, they fire/cancel, you fire & the shroud breaks lose on the code)
And yes console deleting their gateway is basically a surefire way to crash the game almost immediately.
At least the gateway spawning is robust enough that whatever system the gateway spawns in, the yeeter there transforms - only with the above issues of course.

Only fixes I can see given your findings would maybe avoid the fromfrom scope look at country of fleet owner, search a flag and spawn in the flagged yeeter system? - It's not common for players to have multiple yeeters, but I guess that isn't an ironclad way either. Another thought for a similar function is go hard into the gateway making aspect of the mod and unpair it from the yeeter, making your own unique yeeter megastructure with it's own researches, etc.

Couldn't post in main chat... character limit.
Very fun mod though and hope 3.5 hasn't nuked all your efforts!