As for the fridge I think you could use a inverter couldn't you? I bet the largest one you can plug into a standard cigarette lighter socket would power a small fridge. I agree with Don on the thermal electric types not being very good. But, they will withstand a lot of abuse and vibration. And, they're pretty inexpensive. My son was in a similar situation a few years ago when he drove a company truck. We took the passenger seat out and strapped down the fridge there. We wired the inverter directly to the battery bank. Sounds like you might need to switch trucks or the company won't allow such a changes? He broke a few of those standard motorized type dorm fridges I think because of all the bouncing. We switched over to a thermal electric type and that lasted.
As Don said, the microwave is going to need a lot of power. I don't know if you'll be able to run it through the cig lighter inverter. What about getting the smallest Honda generator you can get with a remote starter and strapping (and locking) it to the catwalk outside? Not going to be inexpensive, but should be pretty slick. If you mount it in some sort of protective box it'll keep it in better shape so it will hold value longer. And keep thieves eyes off it.
'03 Freightliner FL112, 295" wheel base, with '03 United Specialties 26' living quarters, single screw, Cat C12 430 h/p 1650 torque, Eaton 10speed , 3.42 rear axle ratio