I don't use sugar. That's mostly because 1) those old NY places I'm trying to emulate don't usually use it and 2) with my oven setup, I don't have trouble getting color on the crust. But if I did, I'd certainly consider it. Can't wait to see what you're making.
I enjoy the added layer of flavor from sugar on other formulas. I'm dialing in the amount. Your formulation does not need it. There's a level of sweetness on it's own. (Sweetness is used for lack of a better word.)
The idea I'm working on got delayed a bit, but will probably find it's way into the mixer this weekend. It's more of a curiosity. A "What if?" moment. Two formulas I'm quite fond of is yours and a sour dough. I take the starter out at an earlier point than normal after the feeding so that acidity level is lower, leaving nice, rich flavor. It's good at 1-day old and handles the fridge well enough to be very good up to around 5-days. At 5 or 6 days, the SD kicks in a little strong for how I like my pizza. The texture is outstanding, though. Different, but outstanding.
We all know what yours will do. The thought to add some IDY and mix it like yours came to mind. The SD is too extensive, so it can certainly handle the salt increase. Oil and hydration levels will work, too. I have no idea what will take over at various stages. I do know others hedge their bets with the starter by adding IDY, so it's been done. What I might have to do is figure out a way for the wild yeast to stay alive longer and not turn into an acidic blob.
So that's why the question of sugar. My assumption is that the right sugar will keep the SD wild yeast alive without sending the IDY into orbit. I've got the SD book by Ed Wood. Hopefully the answer lays within.
I do not expect this to succeed, but I don't learn if I don't try. Besides, happy accidents happen. That's what made me chase the rabbit down the hole after reduced acidity. Never would have known about it had been for a failed experiment.