Take a look at some of the flotation sizes, like 31X10.50 and 30X9.50.

I've rallied with 30X9.50 Yokohama Geolandar MT+ tires and had no clearance issues, so 31X10.50 shouldn't give you any issues under normal driving and wheeling.

As for your insert, normal body repair techniques (bondo or body filler and paint) are an easy fix for cracks. Alternatively you could get it covered with carbon fiber by a local fabricator which would look pretty trick. Just be certain they use a UV stable resin designed for outdoor or marine purposes.