My batts have a 500AH capacity and the inverter
we have says it's good for surges to 2500 watts, but carries a 1000 watt rating.
I've located 5000btuh units with 4.5 amp rating for less than $150... So the cost to be is the unit. I have plywood
to mount it in.
Forget about 8 hous of sleep... It's more like 6-7 max. I don't know how many cycles it would take to maintain the cabin
at cool temps.
We typically run the engine
in the AM to cool the refer, recharge the batts and make some hot water
. I don't know that the high output alternator
could put back in an hour what the inverter
would draw down, but that's the most we run the engine
I may give this a try as it will cost less than $150.