6 minutes sounds like a really long time @620F - let alone 7 @ 650F.
At 650F, I think you probably want to be at about 4 minutes - maybe a few seconds longer. How are you measuring the temperature? Are you getting your stone thoroughly preheated? On the BS, you could also super-heat the stone and then bring the flame down before launching. You also might try bringing your TF down a bit.
My bad. I should not have omitted my bake steps. My posts are entirely too long, and I always seem to leave out the important details. (temp taken center of lower stone more consistently now.)
#1: pre-heat BS for about 3-5 minutes little bit above lowest dial setting. (flame clearing edge of steel by an inch or so)
#2: Turn flame up to about 1/4. About 5:00 for rest of 10 minutes.
#3: Stretch skin, move to peel.
#4: Guesstimate how much more flame I'll need to get lower center stone to target temperature. (Somewhere from 620 to 660 for now)
#5: Top my pie.
#6: Make sure my temp is in the range I'm shooting for.
#7: Launch pie.
#8: Crank down oven dial to lowest position.
#9: Bake until done.
Towards the end of the bake, the area on the stone to the left and towards the front of the oven with the pie on stone will creep down to the mid to upper 500's unless I launch any higher than 650F in the center. I'll take note of pre-launch temps for an accurate amount of decrease on that spot. My guess is it comes down maybe 20-40 degrees.
fwiw, the crust I am shooting for is kind of like that crust you get when the pizza dude throws your slice into the oven for a couple of minutes and the crust is nice and crunchy. I can get there, and I can do so without ruining the outer ring. I can even do it without over-browning the cheese. I can't do it without that rapid bubbling happening too soon and too long.
I can go straight up NY style with not quite so much of that crust crunch. 570F on the BS is a mighty fine place to be, and that is what my fail-safe would be if dinner guests were here. I want better. I've done it a few times. Repeating is difficult.