keep in mind that if you do plug in your shore cord to an inverter, your fridge will most likely automatically switch over to AC, it will be a drain so manually switch it back to propane
if your going to get new or dual batteries I use to have a pair of srm-4d's from interstate, could run my TT for 5 days no prob with a movie each night, lights water pump, exhaust fan when cooking, so I imagine with solar panels constantly charging each day you could run a microwave or other stuff, I doubt the AC though for more than 20 minutes.