Greetings,
I've never been to Yellowstone - we'd like to go one day.
You've already mentioned that you have three possible sources of energy to recharge your small #24 battery: Solar, Truck and built in Genset.
To us, the trick to long term "boondocking" is NOT getting awoke at 3-4AM by the sound of the propane leak detector (most RV's built in "low battery indicator") and the furnace trying to take the "chill" off.
If your going to stay in one spot for more than overnight running the onboard genset (or starting the truck) during the non-quiet times will help keep your battery up. Just check the voltage/charge level and top off as needed while still daylight. :)
The real worries I'd have is two fold - #1 is propane and #2 is holding tank space. (lastly maybe fuel for the truck)
While for 8yrs I had been able to boondock for 1 week at a favorite camp spot with 100-125W solar on the roof and just a single group #27 battery, my holding tanks had to be used very sparingly to last the week.
After the 1st few years of running out of propane we switched to heating cooking/cleaning water in a tea kettle on the stove. (propane water heaters are a close 2nd if not tied for 1st place in propane usage behind the furnace) 25gal of fresh water was usually enough for the week (we showered at campground facilities) however once or twice ran out of water the morning before departure. Heating water in the tea kettle also helped conserve fresh water.
Since I've never been to Yellowstone, I'm uneducated as to where one might empty holding tanks, refill the water tank and where (if any) propane and fueling station (for the truck) might be.
My EWAG (experienced wild ass guess) is that if your using your hot water heater and/or furnace with any frequency you'll have to venture out of the park to refill your propane tanks ~1week into your adventure/trip.
