I think it is time to get 5-day ice chest and ice from local WALMART or LOWES...
Hard to make comments without knowing mdl numbers... All INVERTERS are 12VDC power hungry... A 1500WATT INVERTER will draw around 120AMPS from your battery if fully loaded down. i.e. A typical single GP24 Trojan 24TMX deep cycle battery will only produce 12VDC @ 75AMPs for 36 minutes according to this google image spec sheet.

Sounds like to me you will have a dead truck start battery soon. Then what....
Rule number ONE for me is never ever mess with the truck start battery system - This is the only way to get home on... We always test things out at home sitting in the driveway. A heavy load like this is would also be very hard on your truck ALTERNATOR system with the motor running. You sure don't want to blow that on the road.
Maybe some other campers there can help you out...
Good luck...
Roy Ken