A-Neibs, I bake my pizzas on a 1.25" soapstone slab and can achieve a bake time, at 550 of 2.5 minutes, although I usually turn it down to 525 to get a 4 minute bake. I was, for a while, a huge proponent of soapstone, only to find out that it varies tremendously from supplier to supplier and can be prohibitively expensive in different parts of the country. Steel, on the other hand, is found just about everywhere and is very reasonably priced as well.
The more conductive the hearth, the faster it delivers the heat to the pizza. Steel is more than 10 times as conductive as cordierite baking stones. Although it doesn't bake pizza 10 times faster, it shortens the bake time dramatically. Your baking stone might take 7 minutes to bake a pizza at 550, but 1/2" steel would cut that bake time to closer to 2 minutes. Faster bake = far superior oven spring = light and airy. You probably wouldn't want to bake the pizza in only two minutes, though, so you'll want to turn down the oven to 525, like I do with my soapstone. Pizzeria Bianco is around 3 minutes, so, since you seem to enjoy that, that's probably a good target to shoot for.