Mike, I believe that 'ceramic flagstone' is just marketing speak for 'cordierite.' It's either going to be cordierite or a cast cement material like fibrament. The fibrament tends to be a little less durable, but both should suit your needs. Because the Sage ovens have such a wide range in temps, the only concern you might have with the hearth material is durability, and, as far as I know, Sage ovens have durable hearths. While the forum has a handful of Sage oven owners, it doesn't seem like people have been using them much- at least not in recent years. Still, they've been around long enough that if the hearth was in any way prone to issues (such as cracking), we'd know about it.
Because you have the option to pre-heat the stone to any NY style temperature imaginable, the conductivity of the hearth material makes no difference. While a home oven owner has to reach for more conductive materials such as soapstone or steel to accommodate ovens that can only reach sub 600 temps, if your bottom isn't browning fast enough, you can just turn up the dial and increase the pre-heat temp.
Scott's instructions for using this kind of oven are on the money:http://www.pizzamaking.com/forum/index.php/topic,12165.msg114690.html#msg114690
I don't know what bake time he's seeing with a 625 pre-heat, so it will take some trial and error with pre-heat temps to match your present 4 minute bake, but there will be a number that gets you there. It should be somewhere between 600 and 650.
My biggest concern with this oven and this stone is recovery. This is a thin, low thermal mass stone with an anemic burner below it. I don't know how many pies you plan on doing at once, but, I think if you plan on doing more than 3, you could end up drawing a large portion of the heat from the stone and see long recovery times. You could try putting in a thicker stone, and that may give you more pies before the stone is spent, but it will extend your pre-heat time considerably, and, because of the weak burner, again, you'll hit a wall where the heat in the stone is depleted and you'll have to give the stone time to recover. With an extra thick stone, that recovery time will be even longer.
For making lots of pizzas in a single setting, there's going to be an approach that feeds the stone with heat at the same rate that you're drawing heat from it, but it's going to take a considerable amount of experimentation to find it.
In all fairness, home ovens have these same high volume concerns. Around pie 5, my undercrusts start looking pale, and I have yet to dial in the exact method to prevent that. The only difference is that my stronger burner allows me to feed my stone a bit faster.