Two key differences about what you're proposing: unattended operation and metering of fuel supply. I doubt any builders have grills that are intended to work unattended while the vehicle is in motion. Sure, propane and electric ovens have a risk of burning the roast or, if very poorly/carelessly used or maintained, even starting a grease fire, but they're at least in the passenger cabin where indicators like smoke and burning food is detectable by reliable human noses.
Second key difference: ovens have carefully metered fuel supplies; grills and smokers don't. I may have a huge generator (even a power plant) backing my electric heating element, but due to the voltage being fixed, the element's resistance is such that it can only draw less power in an over-temp situation. Gas/propane ovens have precise metering, similar to carburetor jets or injectors in an engine, that prevent ALL the fuel source being available in a fire situation. (In fact "engine fires" are almost a result of the supply system--a leaking gas line--spraying an unmetered amount of fuel on a hot surface, not something going wrong in the combustion chamber itself.)
Plus it's very easy to install overtemp detection on ovens that cuts off fuel (either electricity or gas) completely. But for glowing coals that burst into flame, or stacks of biscuits that ignite (or hoppers of pellets, etc) you pretty much are left to fairly serious fire suppression approaches to deal with the problem, which I think you have the resources to implement...just don't scrimp on the engineering there, including upgraded insulation.
Again, in short, there's a reason the Bradley literature says 1) keep away from structures and 2) don't use unattended.