I did some searching with limited results.
Wondering if anyone has first-hand experience on what fits a stock height '96 F350 4x4?

 

My '92 F350 4x4 has stock suspension with 33x12.50-16.5's on 16.5x9.75" wheels. All I had to do was shim the front bumper forward about an inch and a half or so and there has been no rubbing on anything, including driving off-road. You should be able to fit 35x12.50's under it too. I don't think they would be an issue on my truck and I have seen a few stock height F350's with 35's on them before. If you do go to anything bigger than 33 though, make sure you have enough gear and engine to pull them.