I stay the night while traveling. All i can add is:
I have a 12v fan running (about the same size you have)and also the 14" 12v tv in the bedroom. No inverter. Still running when i wake up 6 to 8 hours later. One battery.. I am sure, running, i mean, not by much.
Running through an inverter i think your time will be considerably less.
I have since installed two batteries getting ready for a big inverter install.
2001 F250 7.3