Thank you, everyone, for your kind words.
Nick, thickness relates both to recovery and bake time. Even though it sounds like your recovery needs are minimal, I can't guarantee all the possible range of NY bake times with 3/8" steel at 550.
I'm pretty confident it will comfortably break the 4 minute bake time barrier at 550, and, 4, as I've said before, is where the magic happens for NY style, but you might like the extra contrast/additional char of 3 minutes, and I'm not sure 3/8" can comfortably do that.
If you know, for certain, that your oven can reach at least 550 (as measured by an IR thermometer) I think you should just get in under the wire with 3/8", but, if it were me, I'd feel more comfortable with a little more buffer. If you're worried about the flimsiness of the shelf, as I said before, suspend the plate on square steel (or aluminum) tubing. Home Depot carries the tubing and a hack saw will make pretty easy work of it, especially the aluminum. 4 pieces will support the two plates. Just cut the pieces so they go from side wall to side wall.
Besides, once you start making some of the best pizza you've ever eaten, won't you want to make more than 1 pie at a time? Won't you want to share this marvel with friends?