I'm sorry to have to tell you this "but you ARE breaking axles in the dirt" because of the welded diff. It differs in perfprmance on the tar because of the uneven loads applied on rough slippery or hard dirt surfaces. Dirt use is always going to be harder on the diff centre especially if its a little rough or uneven on a hard packed surface.
Only solution is to go to a bigger diff/axles or allow some slip in the diff via a well designed spring loaded locker, or even better as Dodgeman has suggested, an LSD.
The problem will be added to a little because of your soft suspension, tightening the rear up will most likely give you more oversteer and possibly less traction in the dirt. Its always a compromise though!
If you throw another crown wheel and pinion in it without getting your diff set up properly I am afraid that you are only asking for trouble. Broken axle and maybe broken crown wheel or pinion