With only a dual purpose group 24 battery, you will find that you will need a lot more generator time than you think you will need. The manufacturer should have installed a true deep-cycle battery in Group 27 (unless not possible).
Sorry to downplay chance of success, but that battery cannot survive without plenty of generator time. The WFCO 9875 would, in theory, supply up to 75 amps but not possible with one crappy small dual-purpose battery. The converter/charger will most likely not come close to too full capacity. That size charger should be mated with more than two batteries.
Amp outlook may only be about 15 amps per hour of generator time.
The best way to find out who is giving you an honest answer here is to do a 24-hour test at home, or a weekend at a campground where you can plug into shore-power when things go south on testing.