I misspoke earlier. I was considering not a 32" tire, but rather a 33" , 285/75R16 BFG All-Terrain T/A KO for the rear only, rated for 3750 at 80psi. And about the axle ...

Ford Sterling 10.5" Axle Rebuild - Four Wheeler Magazine

"About The Ford 10 1/2-inch"

"The 10 1/2-inch (commonly referred to as the "Sterling 10 1/2") is a full-float axle with disc brakes found in 1999-2010 Ford F-250 and F-350 trucks. It weighs in at approximately 333 pounds in single rear-wheel versions. The ring gear diameter and pinion shaft length are both 10 1/2 inches. It has a pinion shaft spline count of 31 and an axleshaft spline count of 35. Compared to its predecessors, the first- and second-generation 10 1/4-inch axles, the 10 1/2-inch axle obviously has a larger ring gear, which improved its overall strength and addressed the premature failure issues of the of the 10 1/4-inch axles when used with 4.10:1 or numerically higher gear ratios. There are a number of limited-slip and locker options available, and there are even aftermarket axleshafts available."