Travelling 13 hours non-stop with cat in cabin?

Looking for suggestions on how best to travel with my cat from Istanbul back to the southern US, ie, Miami, Orlando, Atlanta. I will be flying in cabin (hopefully business!) with my cat in a carrier. I have a pet passport and the cat is microchipped. I will be getting all required vaxxes (rabies, possibly more) closer to the date of travel.

My concerns: what if the cat "does some business" in the carrier? I am traveling with blue pee pads, but it will be really unfair to the rest of the passengers, never mind the cat, if there is an exposed poo odor throughout the cabin for 12 hours. I read about a woman on a Delta flight who changed the pad (without taking the cat out) and she got in big trouble. I think it's because she took the carrier to the bathroom. Maybe it can be done at the seat?

I was thinking of going from Istanbul to Amsterdam or Frankfurt, laying over if I can find a pet-friendly hotel, and breaking up the journey a little bit. There is a big pro to that, inasmuch as the cat gets to stretch some. The con is that it extends the misery for both of us.

Would like to hear from you all who have done this.