I would imagine that biasing the weight distribution more towards the front would cause more instability in the pigeon during cornering. With stock parts, the only thing you can really do to accomplish this is to remove the bed.
Best way would be to make it more top heavy, so try and remove anything particularly heavy from the chassis in order to lift the center of mass I'd say.
Welded diff will not help as your wheels will spin and break traction more easily. You need traction in order to roll over. You can keep the shocks and coils, but I'd soften the suspension as much as possible, raise the ride height, and remove any sway bars/anti roll bars