If your batteries go from fully charged to 10.2 that quickly, they are toast and need replacement. 10.5 is essentially 'dead'. I can go 4 days (no solar) with my Group 24 Interstates powering just the fridge (on propane), very little lighting, and water pump usage. When they get down near 12.1V, I charge them. You should have better results with solar in the mix.
As far as what to shut off. Your fridge will draw a bit, propane detector is always on, and there are varying opinions that the inverter, even in standby mode, draws a bit. And lastly, the subwoofer, even if off. Others have disputed those last two things. Seems to vary.
A lot of threads on here regarding batteries. Many have switched to 6V golf cart batteries in series and report better results. Trojan T105s seem to be common...if they fit in your box.