When you have hundreds of people all trying to make NY street style pizzas, there will always be outliers who do not know what they are doing or are relying on former owners' recipes or old family recipes or tradition. I agree with you that eggs may not be part of the authentic NY style but how do you feel about honey, or barley malt (dry or syrup form) or molasses?
Peter, I have a tremendously difficult time defining certain aspects of NY style pizza. There will always be outliers with this kind of thing, but, for the most part, the bulk of NY pizzeria owners, both present and in the last quarter century, stick to very similar techniques. One could, in theory, pretty easily come up with a VPN type of document that defines NY style, based upon how the majority of pizzerias are/were making it. It wouldn't be quite as cut and dry as Neapolitan, but, it could still be done. In other words, I could just say, "Here's what the bulk of NY pizzerias do. Do what they do and that's NY style pizza." Piece of cake. Unfortunately, improvements have surfaced in recent years, most notably, multi day cold fermentation. Multi day cold fermentation may have been practiced by one or two pizzerias historically, but I'm certain, because of the walk-in space required, it wasn't a common practice, and thus not part of the NY pizzamaking canon.
The evidence is overwhelming that multi day cold fermentation produces superior pizza- pizza with a more flavorful crust that doesn't sit like a lead weight in the gut. The process draws out inherent flavors in the wheat and additional sugars, so you're, to an extent, magnifying what's already there. If fed a same day slice and a two day slice, side by side, the average guy on the street would prefer the two day, but, most importantly, he wouldn't necessarily see a drastic difference. It's an improvement without inherently altering the original product. For instance, many people like sourdough bread and feel that starter improves pizza dough, but the end product of that process is discernibly quite different. I'm okay with variations as long as there's sufficient evidence to prove that they produce a better product and as long as they don't change the intrinsic nature of the style.
So, I'm working with an 'evolved' definition of the style- which complicates things a bit. It's something that I struggle with constantly, because once you start incorporating techniques that the majority of NY pizzerias aren't using, you're opening the door to other possible 'improvements' and a greater degree of subjectivity- and the last thing NY style pizza needs, as it's global journey exposes it to misinformation and adulteration, is subjectivity.
As to your original question, if I was looking at your ingredients from a strictly traditional mindset, my answer would be "no, none of these ingredients belong," but if I applied the 'improved, but not drastically altered' mindset that I'm using with cold fermentation, I might be open to barley malt. Maybe. Molasses, because of the noticeable change in color and flavor is out of the question. Honey is, imo, too foreign of a flavor as well. Barley malt is a bit different because, due to the barley flour already present in the flour, you're not adding an alien flavor. Sure, diastatic malt isn't going to be as flavorful as non-diastatic, but the profile should be close. In that sense, like cold fermentation, you're bolstering a note that's already there. If one were to use malt syrup or powder they'd need to make certain that the roast would be very light so as to not alter the color of the crumb.
In other words, 'no' to honey and molasses, and a qualified 'yes' to light barley malt powder/syrup.