A little further look into your situation almost seems to be outside of NFPA #13. They generally stack 400% more tires in an area, at an elevation of 15-25 ft., (right in the sweet spot for fire development in storage), and appear to be on tread. 13 requires that tires on shelf be treated as solid shelf rack storage. Since they rotate, it looks like in-racks are out, and you need ceiling only. (CMSA or ESFR). That is going to limit you to what is listed for that application. This information can best be provided from the Manufacturers. Not sure what is out there, but you may be looking at foam included, if even that can be used.....
R/
Matt