If it were to touch where you've chalked no harm as long as its light rub but I'm seeing the covers edge? Hard to judge angle/swing from pic. Diff moves back as well as up. If theres remote possibility that cover might hit at minimum could file cover edge so less likely to cut tire if it does contact. Though pic from bottom looks like a mile of room. If it clears, its right there-lucky.
Running different size tires on drive axle under load I wouldnt do, never heard that recommendation before. Smaller tire goes in the front, even 4wd, very few have front lockers, not near the load. Might be a steering nightmare (pull to one side?) but in rear could be a mechanical one.
Even open differential, can handle the difference but by spiders gears differentiating, as designed,-but constantly. If you have a limited slip going to 'slipping' constantly, full locker you could blow or break an axle, I'm probably propagating old wives tales.