Daryl

I was suggesting the use of the Foster style slugs because they are readily available in weights from 7/8OZ to 1&1/4OZ at several velocities and are cheap. Finding one that brings the two groups together gives you a good idea of where to go with a roundball weight and velocity at least getting you in the ballpark.
You are correct that dropping the weight of the projectile should bring them together. As to adding weight to the barrels that would also work and if you've figured out a good way to do it please share it.