A little bit of a round about way to do this, but you could get a 'solar generator' to plugin to the inverter. The 'generator' then will charge from the truck, have it's own battery, and most can power up to 1500W or so. I run my fridge/camper lights/heater from one of these, that's then plugged into the inverter so it charges back up when the truck is on.
Probably a bit overkill for an occasional use, but I'd imagine it's much easier and even a bit more useful than trying to upgrade the onboard one.