Red Dog, how long do you smoke your cheese? I'm doing 2-lb loaves each of mozz and sharp cheddar. I usually slice them up into roughly 1/2 sections so that they're coated on all sides with smoke. I then vacuum seal them for aging in the fridge. When I'm ready to use them in recipes or just eat them, I can use those individual sections instead of cutting into a whole loaf.
Hope you enjoy your Blackstone oven--please report back on the results. I went the cheap route and bought a Weber pizza stone for my Weber charcoal grill. I gotta get the heat right; last week the tops of the pizzas were perfect but the bottoms were burnt--second time it's happened after a glorious first time success. Weber advised cooking over direct heat but I'm going indirect next time. Wood and coal fired ovens in pizza restaurants get much hotter than my Weber but they use indirect heat. I'm definitely going to try grilled pizza with smoked mozz next.
Probably shoot for about about 2 to 3 hours depending on how warm it is in the morning. I don't want it too smokey for use on pizza. I tried grilling pizza on the weber with the same results. The problem is there is nothing to reflect the heat down on top the pie. I have seen people get good results by putting another stone supported by fire bricks about 5 or 6 inches above the bottom stone. The Blackstone works great. It has a rotating pizza stone with a single propane side burner and another stationary stone above the pizza to reflect heat down on top the pie. The bottom stone cooks at about 700 deg and I can cook a 14 inch pie in about 2-3 minutes.