Chau, from what I understand, Caputo makes two pizzeria flours, the red bag and the blue. Both have a photo of pizza on the label, and while they may not be identical, I believe they're relatively interchangeable. Caputo also makes other 00 flours that are lower in protein, which is what I think the mobile guys were using, and are now using a non pizzeria 00 from another brand. I'm uncertain about a few things- as previously mentioned, but there's not a chance in heck that either the red or blue pizzeria 00 flour, at 60% hydration, and ~17 minutes of mixing, could ever produce something truly tender with 4 minutes of baking.
And, yes 17 minutes, regardless of the mixer, is definitely not minimal kneading.
When you get a chance, try a relatively low protein all purpose (maybe 10%), with a moderately high hydration (for it's absorption value) of around 60%. No oil, no milk. Mix until smooth, but try not to overdo it. I really think that should explain the mobile pizza. Explaining Lucci's, well, that's another story.
Nello's is, without a doubt, high oil- both in the crust, imo, and in the pan. The excess of oil (along with the minimal ferment) is a big reason why it sat so heavy in your stomach.
Dry milk, fwiw, contains glutathione, but I'm not sure what it's buying you here.