I know this is about a month old but in case you haven't done the project yet, have you considered a RoadPro? Very popular with truckers. I have cooked and reheated with it numerous times. Works great. Gets to like 300 degrees I think.
You will have to get a more capable inverter, some heavy gauge wire and a direct connection to the battery. You could also run a gas generator from the bed of the pick up and run a line into the cab of the truck, similar to what was done in the picture.
In my opinion, the “BEST” infrared grill is made from a company called Mark Miller. They originally developed their infrared technology to dry automobile paint. Later they discovered they could use it for grilling. Mark Miller is by far the leader in the industry for that style of the cooker. There is a learning curve on using it because the heat is so intense. Mark Miller also has some cool accessories that some other grill makers do not have like a drop in a steamer basket and a drop in deep fryer