Increasing elasticity of microcrystalline wax
The wax (presumably a mixture of mostly n-alkanes?) constantly re-crystallises under strain, making it brittle in the same direction. Petroleum acts as a plasticiser, easing the flow of the amorphous phase, but also easing the recrystallisation even more. In effect it doesn't really help with your problem.

You could try to find another, harder wax with longer alkyl chains, and try softening that by mixing in your present material.

And generally take your time when working it. When the material becomes less opaque, i.e. whiter, then it is already hardening. Stay below that threshold. High strain rates let the crystallites grow, which are stiff, so at the edges of the crystallites, the strain rates are even higher.