I find it amazing that you have managed to get the groups 8" apart at fifty yards with a bore size round ball in a 7.5lb gun. That is a heavy projectile in what have to be reasonably light barrels.
From my experience I think you've reached the upper limit of what can be accomplished by reducing barrel time by increasing velocity. For what it's worth I haven't found that weighting the butt has much to do with bringing the groups together. What would need to be done is to add weight to the barrels and I don't know of a good way to do that.
Have you tried the common Foster style slugs? I know all the arguments against them but in 12Ga there is enough variety of projectile weights and velocity that you can get a good idea of what weight round ball you might need to go to and at what velocity.
I seriously doubt that unsoldering the barrels and trying to regulate them will work with that heavy a projectile.