OP, good explanation of the situation.
Have same problem with our TC for battery space and MW operation, but not the weight issue. You want LFPs for the weight, high discharge rate without alarming off the inverter, and more AH, while any gen time reduction is a bonus. Got it!
Fixed ours with a pair of SiO2s (act a lot like LFPs) for half what LFPs cost around here, but you could save weight with the LFPs. No temperature issue with SiO2. LFPs are coming down in price in the States maybe so that could help.
Had trouble with our battery compartment being able to hold two 6s but not two G27s. With AGMs/SiO2/LFP you can stack them on their sides if that works. Not with ours. Moved the batts to inside the camper under the closet floor since these batts don't need to be vented as much as FLAs. Your camper might have an opportunity somewhere inside to move the batts to if you need to. That would help solve the temp issue with LFP and keep the weight saving value.
So you are right to be looking at LFP for the reasons given. You might be able to get the same benefit from SiO2 if you can stand the weight being like the 6s and not have a temperature issue. LFPs have a longer "life" in terms of cycles you can do, so if you are young that could even up the Money part. (Any new battery could outlast you if you are getting on like some of us :( ) We are too old for LFP.
On that, there is the question of how long with that RV and what happens with the LFPs when you sell it. Have to yank them out to put in your new rig and get a FLA to put in the old rig. So leave some wiring in the old battery box if you move the batts to inside.
Some solar might help too. It does not weigh very much and can bring in lots of AH.