I tried another variation last night that turned out well (in our opinion, anyway!). Used the griddle plate on the grill, and basically just added some thickly chopped lion's mane mushrooms to the sautéing onions and peppers, and subbed aged Swiss for the provolone.
Not your traditional Philly, but I liked the smooth flavor added by the Swiss, which paired well with the mushrooms. People don't often think of wine with a cheesesteak, but since I added the Swiss to both the peppers/onions/mushrooms and steak, I tried a little Pinot Noir and, bam! it brought out the flavor profile of the cheese and mushroom mix.
Anyway, just had to report my tinkering last night. 