A couple of yrs ago when took the kids to the states, the youngest was only just 2 and quite small for her age. We had the same dilema of taking the car seat (we took both seats as car hire firm couldn’t confirm availability, even if we had paid for them :-/ ) , in the end we decided that it would be easier for us not to use car seat in the cabin. We figured that by using the seat she would have to sit in one position for the whole trip, instead she could sit, lay down, wiggle non stop and had a great flight.
With all that luggage do yourself a favour and get a porter to help, best money i spent all holiday.
PS we did see someone using a British airways child seat on the return trip, it was massive! You wouldn’t to squeeze past that to many times for a wee etc.