K.L.
I also have a "terrible" two-er - and I am also slightly crazy. We should talk!
We call this face stuffing/choking/spitting out meal and snack deal "cookie monstering". My two year old has been doing this on and off for the past year, and I swear, half the food she eats goes down mostly, if not totally, whole - the rest of it ends up in a half chewed gob of food that she spits out sometimes into my hand, sometimes spits in little pieces on herself. Yeah, I know. She seems to really enjoy doing this, and the more displeasure I show, the more fun it gets to her.
She is an excellent eater, and feeds herself most of the time, but seems to do this cookie monster thing as an attention getting ploy. She is quite the naughty one. I always try to give her small portions of things at snacktime, making her finish whatever she has in her bowl first before she gets more. She feeds herself at mealtimes, but I always sit with her while she eats to nip the cookie monstering in the bud if it begins. At that point, the meal is over - she does it when she really isn't hungry anymore or wants attention more than she is hungry. I don't care if she gets upset, all the food goes away once that sort of behavior starts, same with snack time. I discourage it not by yelling at her (because they just find MORE joy in the behavior when you show any sort of reaction, negative or positive) but by just removing the problem altogether.
You can try to keep them from doing it, but expect it to happen on and off. Its kind of a kid thing, but you can definitely discourage them from doing it by removing the food.