If you pulled the ring and pinion gears out in pieces, it was not the tires that did it. If they broke up that bad, more than likely someone did not put them in right with the proper backlash or pinion gap.
If set up right it is hard to destroy the ring and pinion gears, unless the fluid never got changed in 40 yrs or it got filled with water and rusted all up.
Roundhouse is right, with your set up 4.10:1 gear ratio would be idea for your truck. If you wanted it a little more highway friendly you could go with 3.73:1 ratio.