Sounds interesting, I've never had squeaky pizza, but I've had many squeaky poutines ( French fries, bbq gravy and cheese curds ), it's big in Montreal, cheese curds are sold in little hand-size bags at all corner stores, Costcos, grocery stores....
however -- curd cheese is VERY expensive up here, vs mozz cheese...... so I've never even come across a pizza with curd cheese, but I wonder if the place you went to as a kid was maybe using
a combo of cheese curds ( poutine cheese ) and reg old mozz cheese.
When I was a child, my father would always bring home pizza for supper on Friday on his way home from work. At place called Hotlips in Newmarket (Ontario Canada) had what I thought was the best pizza around. The edge of the crust appeared to be made of 2 pieces of dough twisted around and somehow joined to the base (which seemed like a different kind of dough). The cheese was the big thing for me though. It was very thick and very rubbery - never stringy at all. It just about squeaked when you bit through it (like cheese curds). Does anyone have any idea what kind of cheese that could have been? It was white, slightly salty and mildy greasy as I recall.