I've done just about every senerio mentioned and for what it is worth, I'd just rent one from the car rental company for the short time you will need one.
On my last trip to FL, I had to rent both a booster and a car seat. Both were in the car, in plastic bags for me to install. While I'm sure car companies do everything they can to save money, I can't imagine that they'd re-use a car seat that had been in an accident. Especially, when with insurance they can get it replaced.
Gate checking or counter checking a carseat - yep, it's going to get tossed around just like luggage. However, if you've ever watched them load/unload the luggage, overall it's not tossed about that much. The damage that most people experience is due to the luggage itself being just cheap luggage, old or overpacked. The tossing around that the carseat will get is just like the tossing that is done when it is shipped to the store or from you lugging it in and out of the airport.
Since you are flying, if you haven't already booked your seats, try to book with an empty seat between you and DH. This will give you a better chance of having an empty seat and being able to use your carseat on the plane. We did this for our trips to Paris with our son. I didn't have to buy him a ticket due to his age, so we booked our seats skipping one so there'd be an empty one between us. We were able to use our carseat and our son slept wonderfully.
HTHs!