Um....
There are two things that I would suggest.
1. You could get a longer bolt for the stock spare tire hanger inside the Jeep and mount the 31 on that. It may be a little crooked, but it holds tight.
2. I would use bungees INSIDE the Jeep cargo area using the stock tie downs. I did this for my 33" tire. Worked like a charm.
BOTH of these - no damage to roof!