@6Tap
Your pizza/calzone does not look too bad, I would eat it. Glad to hear it tastes good and you were able to salvage it.
When you say stone plate are you talking the pizza stone? Don't think you want to do that.
You can build and form pizza on a metal pizza pan and don't use the stone at all. A slightly lower like 450 or 425 and a little more time makes a decent pizza. Using a dark color pan helps with browning.
Look back at some of applescrap's post he forms his pizza on parchment paper, makes transferring easy. I have never used that approach but it seem like a good way to do it with sticky dough. I am guessing you can slide the parchment paper out from under the pizza after a few minutes once the crust sets to get a crispier crust.
If you want to try cooking on the stone this might help,
Sprinkle a decent layer of corn meal on the peel(a nice single layer but you can still see wood, but more is better than less). If you got the right amount of corn meal it works like little ball bearing to help pizza roll off of the peel.
Form your crust on the counter then gingerly transfer to the corn meal, get it closest to the edge of the peel.
Work quickly now so corn meal does not suck up moisture.
Build your pizza, try not to mush down on dough too much.
Transfer to the stone is not difficult but it is a little tricky in that once started you cant really stop.
Hold peel at about 20 to 30 degrees (not flat not too steep) as you put it into the oven.
Position just before the spot you want pizza to land(closer to door in oven) with forward edge of peel close to stone.
With a short jabbing thrust like motion get the pizza to start sliding off the peel onto the stone and draw the peel out from under the pizza. This should happen in a fluid motion don't dilly dally.
Sometime it requires a little wiggle of the peel and an increase in the attack angle of the peel as you pull it out from under the pizza.