Never tried on pita, but I’d take a hoakie and slice it into 3 layers (just 2 ends up being mostly bread) and do it that way, too.
Think it was AB (as in “Smokin’ and Grillin’ wif”) who made 'em that way, on 2 layers, but had so much stuff on them that I don’t think I’d have any hope of them heating through without burning the bread at the bottom.
When I do 'em on a hoakie, I’ll toast the bread first so the sauce doesn’t soak in too much, add the sauce, retoast to thicken it (adding sort of a sun-dried tomato vibe to it), then add the cheese and whatever else, then toast again 'til done.
Other than pepperoni or onion-hair or some other ingredient, that’s the limit. When I tried a sort of “deluxe” pizza with onion, olives, pepperoni, peppers, etc., everything on top cooked somewhat, but the cheese wasn’t melted and still “raw” underneath. You really gotta cook it bottom-up as well as top-down.
So in that case, maybe pita might be worth a shot, as long as it’s not eating no-bread-all-stuffing, which is just as bad as all-bread-no-stuffing.
As for EMs, if using only sauce-on-bread, cheese on top, only mozz does it for me.
If using a slice of tomato on top, cheese-on-bread, then mozz, murrcan, monty, any kind of cheese works well.
