I'm not terribly familiar with TC, but I'm assuming it utilizes a converter/charger for the 12V system. I don't think a 500 watt generator would run the converter at full load. I won't plug solar too much since you say up front you're not interested, but I do say you will need a bigger generator in order to run the converter to recharge the battery/batteries.
Based on the volume of boondocking you do, a minimum of 2 x 12V or 6V batteries and converting all lighting to LEDs would be what to start with. I'd shoot for 150+ Ah storage capacity. I see a nice fridge in the website pictures for that TC that I'll assume is 2-way (gas and electric) and will be a source of parasitic draw. So even if you use LED lights and water pump sparingly and no furnace, there will still be a drain on the battery. So a bigger generator for running the onboard converter would be a good idea (or solar, just saying...). I guess you can always fire up the truck to provide some trickle charging, or maybe upgrade the charge path from alternator to maximize that charging potential, but it will still basically be a few-hundred-horsepower trickle charger. With 2 x 12V or 6V batteries, I think you'll get by without needing recharging for your 3 day trips if you are stingy with your power use. But for those "disappear off grid" trips you've described, you'll need a way to recharge those batteries at some point.