I'm still puzzled. Inverter draws 45A. Solar inputs 35A. Battery supplements this with another 10A - and stays in Float. Voltage doesn't drop. Hm... For how long? We know that perpetuum mobile don't exist, right? :)
Yes, these little window shakers are within capability of solar. Though 50A solar would be about 700W, at sea level. It's easier for you in the mountains, less wattage needed. Down here when it gets hot, it's usually hot in the night too, and then I can't see myself surviving even with anything less than 1,200 BTU and there is no solar in the night.