Your mistake was the quartz behind the range not the range .

Weve come to realize that the hard way unfortunately.

You could do a nice stainless back quard but it will transfer heat to the quartz behind it .

I have not dove into research yet, but would an electric stove fix the issue? I know they sell a metal back guard for the stove we have, but if its not going to matter much, it seems silly to buy it (unless thats my best option since replacing the quartz would not be my first choice).

IMO there is no way in h--l I woud trade a gas stove for an electric I guess you could do an induction one but honestly cheaper to change the backsplash than to buy a new stove and upgrade the electrical to handle induction and honestly that is the only choice to change the cooking appliance from gas .I d not understand why you just dont get the proper back gaurd and remove that piece of quartz then.

A stainless steel sheet that is on stand-offs separating it from the quartz might keep the temperature there down (as well as the temperature behind the quartz below the limit for wood deterioration. See IMC section 308.4 for ideas. Note that DIY thermal protection may not meet UL requirements. Even without oven venting the gas burners represent a hazard if the wall is not properly protected or constructed. See your range's installation directions for further information.