several hundred for a multi stage converter may be overkill for a light use rig
many have reported that the cheap battery tender can totally discharge your batts and kill them if shore power goes out for a while. this sounds suspicious, or maybe it was an oversight now corrected. for a hands off approach to charging, check into this possible killer.
simple converters like the parallax units do reduce the charging amps as batts near full charge. in a hands-almost-off scenario, i'd put a note on fridge to charge on 1st (and 15th if you really want happy batts) for 24 hrs, run whatever you want, but turn it all off when the charge time is up.
batteries should not boil, and this should work well for your batts that may be saved. total cost is $0