Typically you don't want to go much more than 4" wider than the rim, the 10.5 is just over that. I think there have been some on here that have run that size combo (justwork perhaps?).
The snowflakes are 15x6.5 & 16x7 if I'm not mistaken, so you can run that size 31" on the 15" no problem. I think something like 246/65r16 would get you close to 31" on a 16" rim.
You can find the 15" snowflakes on Amigos, pickups, and 1st gen Troopers. The 16" snowflakes came on Rodeos and Passports.