Hi,
If you plan to boondock in the desert get a solar system.
12.7 is clearly not enough. Likely the battery bank has never ever been fully charged. It can take 168 hours of shore power to get the job done, depending on the converter that is in use.
The load of 6 amps in twenty-four hours = 144 amp-hours. Add in some lighting plus an hour of run time for the furnace probably adds another 26 amp hours. So the bank is down 170 amp-hours by morning.
Recharge time on batteries is fairly quick until 85% state of charge is reached. Then it drops off fairly dramatically.
Since you probably have 464 amp-hours of storage that means the last 15% of recharge time starts at about 70 amp-hours. To replace the first one hundred amp-hours would take my system about 2.5 hours (assuming night time with no solar help). To replace the remaining 70 amp-hours would take about 5 additional hours.