A person from the Nutmeg state, such as the OP, would never order a Chicago-style pizza. (And really. Can we give it another name? It is a perfectly legitimate food product. But it ain't pizza).
I too grew up in Milford and Pepe's was a weekly ritual. We still go quite often, but find ourselves at the branch in Manchester more often these days. As stated, there is nothing in WDW like it, but that's OK, as there are few places in the entirety of the United States that can match New Haven for pizza. That said, I have eaten the apizza at Via Napoli several times and have enjoyed it. It is good enough to keep a Connecticut pizza snob satisfied while in Florida. It won't compare to what you are used to, and they don't make a White Clam. But it will fill the bill when a pie is needed.