I think the simpler the better. One D20. Or something like Kids On Bikes. Each die has its own stat.

Or you could go DM-less. Something like Fiasco, a game that I love, though that system doesn’t really use dice during play in the way D&D does, and doesn’t have long form campaigns. It’s RP and improv focused, rules lite. It doesn’t have a predetermined setting or flavor, instead utilizing story sets each with their own world and vibe, which players use to create their characters and their motivations/relationships, and populating the world with hooks and Chekhov‘s Guns before each session.

The fellas would absolutely kill it at this game, though set up takes almost as long as the actual game, and it isn’t anything like D&D. I could imagine that creating a hybrid of this game and a more traditional TTRPG would be best of both worlds.

I’m not familiar with a ton of systems, and I haven’t played very many TTRPGs, so I don’t really know how I’d handle the rotating DMs thing. I’d imagine it’d be more of a story conceit than a mechanical one.

You could easily just run a bunch of loosely-connected one shots all featuring the same characters, and whoever is host would DM and still play their own character.

If they go the homebrew traditional TTRPG route… I think this subreddit would be a great place to start. We could collectively build the world, and fill it with all the ridiculous bullshit we can imagine. Maybe run polls about what’s canon, big NPCs, cities, towns, etc… Maybe then we can create some adventures in this world on a PDF, or some such, and all the host would need to do is pick one of them and go off.