At 100F, your spec 14.7v at 77F is now 14.39v and the float 13.6 is now 13.29.
The storage voltage of the converter is 13.2, which would work, but since you are using the camper, it will stay at 13.6, and not drop to storage voltage. Batteries will lose water at least staying at 13.6 at 100F.
IMO, disconnect the solar, disconnect the batts (by removing wire from post, not with the disconnect switch that does not disconnect everything), and spot check the batts with your hydrometer. That will tell you when to recharge them again (solar probably better for that ).
