So I've bought a gas-powered pizza oven reminiscent of the Ooni Koda 12. It gets the crust done alright, but as I expected earlier it is quite difficult to rotate the dough using a peel without ending up with some parts burned and without an overall unevenness of baking level. I've looked anywhere but couldn't find enough information on how to construct a (non-motorized) rotation mechanism into a pizza stone which could healthily withstand temperatures of 500 Celsius and perhaps a bit more. Possible issues I suspect: pizza stones are cordierite — I don't think it can hold screws; so you consider gluing — is there any chemical glue which doesn't release toxic fumes at such degrees? And then considering the types of bearings available — most don't mention it but aren't they likely oiled with stuff that, again, might prove unhealthy within a gas oven? I suppose this question isn't exactly food related, but I haven't found a definite SE category for this. 
The intention behind an oven is to keep as much heat for as long as possible. There are even luxury ovens which are intended to never be turned off, and always use a constant temperature; communal village ovens used to work on the same principle. Modern ovens are rarely built that way, for several reasons. But still, you can expect (or hope) that the heat saved in your well-preheated oven is significant, and that "the amount of heat the oven continues to add to maintain the temperature" is the negligible one. So I would assume that the new dish will get heated much higher than per recipe. From there on, it is a matter of your dish's temperature sensitivity. If you place a cheesecake or a piped meringue into your overheated oven, you are asking for trouble. But if you are, say, roasting a pumpkin, then you probably won't have much trouble from the initial high heat. For a steak, you will likely be finishing it on a pan anyway. Just use a thermometer to make sure you don't have too high a temperature gradient between the deep and superficial parts. 