That Hawaiian named one you linked is a start. Is that the style of pit in your crosshairs?
If so, you could maybe work 2 of that type into their "war wagon" example?
https://www.easttexassmokercompany.com/the-war-wagon-bbq-concession-trailer
Shown with a 1000gal, 15ft length pit. Swap that for the rotisserie style, if that's the preferred pit style. Either way, They can rearrange to get enough cooking capacity for "max", and still be able to handle "average" with one pit lit off.
There's more added to that one than you need, like I don't think you need the actual concession stand equipment, so there's room to customize/pare down as needed. The warmer, fridge, prep space, shitter, sinks, etc could be of value.
Something in that ballpark would work for both away and home, and playoff events as well.
The range may not be needed, or maybe they have another type with less stove burners and more griddle space. Or a grill/griddle type deal. Not sure if the ovens would ever be useful, guess it depends on what you've got on the menu. But for that many people, I guess it opens up some other menu options that might help. (Biscuits for an early game, desserts, whatever.)
The additional space/functionality may prove quite useful on away games. More space for storage, etc, since you'll have to take whatever with you. With the generator, you can keep the meat in the fridge while traveling. And if the concession/serving space is rearranged into something more useful, maybe 2 fridges, and 2 warmers would work better? Smaller ones just use half?
Sorry, just spitballing again, and going off what you've mentioned as needs/wants. Seems like a lot of fun. Even being a shitload of work, it's a labor of love. I think you could maybe get by with 4 people running that setup. 2 with main focus on pit(s), 2 with main focus on handling the pre/post cook stuff as well as the in-between stuff. Not that more help wouldn't be appreciated, but at least it isn't quite to the level of needing an army of support just yet.
I can see the potential you're looking at, and I think you're headed in the right direction. First is getting the costs (overall, in the long run) down, which even with something like that big ass war trailer, seems quite probable in a shorter time-frame than not, given your big picture numbers on food cost. With the difference between the actual food cost and what it costs fully prepared, you seem to have a nice window to play with to get that difference moved to your own setup.
Whatever you do, whomever builds it in the end is definitely going to showcase it. I could see it being one of those things people look for, see it on the road and know Surly is headed out to fuck shit up. As Sheriff Buford T Justice once said, "That's an attention getter." And your idea here has exactly that potential to grab attention and draw eyeballs. That's what can lead to additional sponsors, further helping to curb the out of pocket front.
I dunno, I'm pretty excited for y'all to be growing and able to be talking about doing something like that. Things have come such a long way since way back. When the Co-Op statues were the big talk, who'd have thought such a collection of miscreants would end up where things are today.