you wouldn't have to touch your inverter, the converter yes but that is cheep.
and the little bit about the primary function of the genny would be to run the AC, that little tidbit would have changed 90% of the answers you got and should have been in the original post, not "to keep the batteries topped up" yes LiFePo4 batteries would be a great addition giving you a lot more capacity .. for examble, to get any sort of 5 year life or longer out of a lead asid deep cycle you have to keep ypur usage below 50% of the capacity. a LifePo4 you can use all 100% and still get 4000 cycles which would be 20 years for the normal person, 10 for a power user (these are just estimats) changing the converter would be benificial either way, the converter of a 20 year old van could be deicent, but old and tired depending on use or it could be an old two stage, so going with a larger amprage converter that is Li capable will let you carge faster and more efficiently on your gen run time.
so lets say you get two 100AH Li batteries to replace your who knows what kind of flooded battery. so the ones that come with most trailers are 80ah batteries so 2 gives you 160 but you can only use 1/2 so 80ah capacity, the two li will give you 200ah capacity, so you can go almost 3 times longer before recharging.. also due to the lower internal resistance of Li they charge faster and more efficiently and don't have that slow aceptance phase in the top 20% like normal bateries. another thing you can do is try find sires on the ends of row and then run the power cord into the bush away from everyone else to minimize the noise to others. this alone might make a huge difference as honda's are usaly fairly quiet.
