Battery draw

Battery is shot. My guess it that at some point it sat discharged and sulfated and has permanently lost capacity. Lead-acid likes to be tip top fully charged when not in use for best life. Also don't let it discharge much below 12.2 volts. At this level it needs recharge asap.

I recommend two group 27 or two GC2 (6v golf batteries) as a minimum for off-grid camping. With conservation and minimal furnace you should make two nights.