On our 12" wide wheels with 6 lbs of pressure my D2585's have 1 1/2" from the rim edge to the sidewall.
The less tire pressure the more the sidewall "bubbles", less tire growth. With only a couple pounds of pressure my tires where at 2 1/4"
We make about 900 hp with our Heritage Jr Fueler, and need the 12" rim because with the 11" rim it would get loose at about half track. We ran 10" rim for about 8 years, which gave us more tire growth, ie less RPM at the finish. Are you sure you need a 12" rim ?