I personally don't think stiffening the barrel will automatically improve accuracy.
By adding weight, changing stiffness, adding or removing barrel supports, what you are effectively doing is changing the natural frequency of the barrel.
I'm not sure, but I think what you're looking to do is to create a node point at the end of the barrel, I.e. Have a point at which the barrel is neither moving up or down, so that the pellet leaves the barrel with no off centre forces acting on it.
That can be achieved by increasing stiffness or by reducing stiffness, adding mass at various points along the barrel, or removing mass, increasing the grounded locations (I.e. Barrel supports) or removing them. It will be different for every barrel.
The only way you'll know for sure is to try it.
By the way, I think a lot of the positive effect of many muzzle flips is the damping characteristics that come from their mass rather than their air stripping ability.