I thought the same thing as you, so over the weekend I looked at the MT Sportsman tires and they are TALL for a 12" wide rim. Like 4" taller than the 345/35's!
I thought about going to a larger diameter wheel since 15"'s just aren't as popular as they used to be, and so when I called diamond racing this morning and asked, the largest wheel diameter they do is 16" and that's not as popular a size as it used to be either.
Montezuma, what size wheels/tires are you running on your car? Still 15's?