I would run the Honda all day, I have my two running right now and they have been going all day and the one has been going since yesterday morning. Wife is doing laundry today so i fire up the second one for additional power. This is your easiest way to do things and you already have the Honda anyways. Still install the pads and set them for ac voltage, they probably only draw a couple of amps if that while on ac setting.
Your Honda will run close to 20 hours at idle or under 1000 watts of supplied power. When the Honda is supplying full power, your tank will run dry in around 7 hours.
Add up what all your pads consume on 120 vac and that will give you a idea of how much of a load will be on the genny.
If you have 4 or 6 deep cycles, Iota converter chargers are the ones that I use. Your onboard converter charger is very likely too small to recharge that many batteries, your looking at a 8 hour charge rate minimum, depending on how much you draw the batteries down.
Likely your unit only cames with one battery, so winter camping and running the furnace and a few lights will kill that fast, even if you start off with a fully charged battery. You could get by with firing up the genny early in the morning to recharge the battery and get the heat going again. But a pain in the butt. Being a new trailer i would have them delete the battery and at least invest in two 6 volt batteries, either Crown or Trojan.
Temporary skirt is going to help with your tanks not freezing, adding a Mr Buddy heater along with the skirt will help alot. More gear to carry and setup though.
I had the Agm batteries, orbital type, big bucks and sitting on my shop floor useless. Replaced with Crown two and half years ago and they work really well. Remember I am in the cold Ontario Canada, and cannot afford a breakdown, off the grid for power and water.
As for enclosing the underbelly, some sort of sheeting will be needed, I don't recall what it is called, then regular pink insulation, stuff everywhere. Your valves and drain pipe will likely be exposed depending on your setup, but heat pads or trace lines will work there.
I guess either way your spending money on fuel for the genny or propane for the furnace and aux heater. If it were my deal, I would gear up for running it all off the genny, change the oil, fill er up and enjoy camping.
I should ask, is this a regular pull trailer or fifth wheel, how long, any slides?????

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