Gtsum2, in most instances, cold fermentation increases a dough's sugar content. More sugar = more propensity to burn. You could, in theory, bake a same day dough at 700 and not burn the bottom, but, since your goal is a crisp crust, then you'll want to be going with lower bake temp/longer bake times, not higher/less.
High heat/high-ish water promote oven spring, but they decrease crispiness. What you witnessed this last batch was the superior oven spring you get from short baking times. What you're going to need to do is dial back the heat/increase the bake time until you find that happen medium of good spring and good crispiness. I would try 4 minutes, which with your setup, might be somewhere in the 600 realm.
The one thing that I would stick with is the low thickness factor. As you witnessed, you can stretch a pizza really thin and still achieve a thick puffy crust.
Regarding the damp rag- it lowered the temp of your hearth, which, in turn, gave you a better hearth to dome heat ratio. I think the damp rag technique is a good one, but... I'm not sure it's ideal for use with a primo. This is a glazed stone, right? A damp rag can involve a good amount of thermal shock for a pizza stone, and, although I think cordierite might do fine, the glaze is not that thermally strong. TBH, I have no idea why anyone would put glaze on a baking stone. Glaze is extremely close in composition to glass- and glass is about as thermally weak as you can possibly get. Anyway, I'd seek out a piece of unglazed cordierite or soapstone- those should hold up better to wiping with a damp rag.