I think it's important to know (since I'm obviously not a posek), are there truly any Rabbonim that if called right then would be like:
Passenger: Rebbe, DW and I just boarded a plane and we realized we're seated next to each other, despite being told we'd be across the aisle. She's a Niddah, what should I do?
LOR: What are your options?
Pass: Make a fuss and demand that other passengers be moved to accommodate us. Deplane, and most likely inconvenience the entire plane, crew, etc. Or sit and be careful regarding the harchakos.
LOR: Well, can you politely ask and FA and other passengers to accommodate?
Pass: Tried that, and no dice.
LOR: Ok, you must deplane.