Go solar and forget about worrying I built mine for less than a grand. You have the spendy stuff already all u need is a controller and a couple panels and your all set. You could be all in for about 500 bucks best investment a rv could have and less maintenance on batteries I ended up with agm and they stay charged to maximum at all times I just leave inverter and all the vampires running
Using a big genset to charge the battery is a complete waste of money when boondocking and takes hours to charge back up I ended up turning my convertor off the solar controller is far more advanced technology then the converters
Read bobs the solar guy best thing I ever read followed his recommendations to a t and it's not a trickle charger it's a reliable power plant I'm only using 300w and it's more power then I can consume
By the way 13.3 to 12.5 is a huge draw for one day something good size is pulling it down a memory wire or radio display won't take it down that far look at a fan and is your heater thermostat totally off at night the heater could pop on and really drop the batteries
I can watch TV run all the lights and have the heater ggoing over night and i wake up to 12.5 to 12.3 end the day with about 13.8 and resting at 13.3 if i don't use any power the vampires won't even drop the battery below 13
I'd like to add in on mine I have a charge back wire from converter to an isolator block (Check that) then the wire needs to get to your batteries check for a bad corroded or missing dangling wire my converter is under the bed and batteries are a ways from this area check converter output first