You may need to double check monsters (and associated decks) before running the 4 to make sure there isn't overlap there. I'd be more concerned about multiple guards or archers or something.
As long as you use the app, that should resolve the on main logistics issue (monster attack deck).
Do note though, that part of the requirements to play the solo scenarios is having 2 or more characters retire. So the odds of playing with the starting classes is unlikely (unless you create new characters for this purpose).
That's true. I was mostly wondering if the scenarios tend to use different map tiles and enemies, or if they are all more similar than that. Sounds though, like it might be workable for at least a couple at a time, maybe sometimes more.