Why would Identogo, an official fingerprint contractor for the State of New Jersey, offer fingerprinting services at their Pennsylvania locations under the code for NJ firearms transactions, 2F164B, if New Jersey was going to refuse to accept the results? I'm calling BS, HS, MS on that one. Sadly, that comports with most of my experiences on Reddit - there are far more posters with nothing to offer except attitude and opinion than there are posters who have actual facts.
The info from the State Police clearly states you can carry any firearm YOU own, but not one owned by anyone else. So, yes, you need only qualify with one, instructor's discretion to list others, when I took the class, it was said he wasn't sure about adding one later when I asked about a 4th firearm, I had on order but not received.