Vetri is the real deal. I've had pies in the oven for 2 minutes or so (sitting at the bar and timing it), so, I would not personally say 90 seconds would be a rule for me. The pizza is always A or A+ Neopolitan.
Vetri also has an upscale restaurant called Osteria which serves basically the same pies. (3 locations with incredible WFOs - love it). I have not been but I am told the pizza is the same and awesome.
Nomad is also incredible, in fact perhaps more so. There are two in Philly - make sure you go to the one on Bainbridge (near South St.) NOT the one in the gayborhood called Nomad Roman. Nothing wrong with that one, in fact more upscale dining room, but yeah the name says it all - Roman-style pizza. Very good though.
My only reservation with Nomad is not to go too early because it fills up with families and little kids. And since it is "family table seating" you have screaming kids next to you. If that is your thing have at it. The pizza is always A or A+ Neopolitan. There is also a food truck (maybe where they got the name?) and it is also excellent in every way.
Stella is very good but I have only been once. Nice interior, very Cinzano/San Pellegrino. I would say my margherita was authentic Neopolitan but that is all I had so far. My pizza was an A.
There is a food truck called Pitruco. Look it up on Twitter. Very much worth tracking it down if you are in town and still hungry. I've had B+ and A Neopolitan margherita from Pitruco many times.
You might like Bufad on 13th and Spring Garden. Not exactly Neopolitan but in the spirit of, nice little BYO and not crowded. Also have special Grandma slices and they get quite creative.
There is a place called Zavino's on 13th in Midtown Village. I went once, for lunch, on my birthday because I heard good things. Very underwhelming margherita. It was pretty darn authentic Neo but I was one of the first pies out that day, maybe, and the pie man was not awake yet perhaps. Not nearly enough squish and chew and the general impression was meh. The salad I had though was great. There is another location in University City and maybe that is the one to go to. Nice little dining room on 13th and this is a major party street so you can have a lot of fun after pizza in the bars.
Now, Beddia. I have been 3 times, all before the Bon Appetit article so my reviews would be over a year old at least. The three times I went I was very underwhelmed. The first time I went I would say B- at best. We had the standard cheese. Crust was way too charred up and crispy for me, sauce nothing to remember at all. Nothing like Neopolitan or boardwalk pizza or ... anything really. I just didn't like it. Fancy NY style with burned up crust. I got dragged again and would say this time it was a solid B on the standard cheese pie with arugula. We also tried the arrabiata and it was tasty (better than the cheese) but too unique and I would honestly never get it again as it was too hot and weird. I had a standard cheese again later at some point and it was a B+ and I was like, OK this is way better. All 3 times though the crust was way, way overcooked for my tastes. Very little chew. My friends left pizza bones and I did too. I NEVER leave bones. A puffy cornicone is a cherished mouthful and Beddia did not have this. They had burned bones.
Still, I want to get in line early one day and try it again. Oh, it's $25 a pizza or more. 16" in size-ISH. They seem like nice young men, making 40 pizzas with love a few nights a week, so hey, try it if you have a few hours for parking/line/wait/etc. Basically take out or sit on curb.
I would just go to Vetri, Stella or Nomad and enjoy myself if I came to Philly looking for Neopolitan pizza.