For the November trip I would just install a small inverter in your entertainment center for overnighting at Walmart or other similar overnighting sites. We could power our HDTV, HD Sat receiver, bluray dvd game console, soundbar, and charge all phones or tablets using our 300 watt inverter with room to spare. We have a pair of golf cart batteries and a couple hours of inverter usage hardly puts a dent in them. Your batteries should be in decent shape upon arrival if they are indeed receiving a charge while towing.
That being said, we have a couple of generators as we do most of our RVing off the power grid, often times in extreme weather where our solar array does not always keep up. Our rig has an onboard Onan and 3 years ago we picked up a Champion 3100 inverter genny with remote start being accustomed to one button power on and off simplicity when genny power is required. Running a portable genny at Walmart is fine as there are no rules that prohibit their use, the fact they can be readily taken is a major concern.
As it pertains to future boondocking, your best bet is a multiphase solution that includes sufficient solar and 12 volt reserves in addition to whatever generator configuration you decide to buy. Having a smart converter to ensure quick recharging will certainly reduce genny runtime, incorporating a psw inverter for low powered 120 VAC items reduces it even further. There are dual fuel generator options if carrying gas is an issue, although propane will be more costly as it is consumed at a much higher rate by comparison.