Magnum mount issue?
I wouldn't run it any more than it takes to test it out to see if it still has the vibration. Vibrations like this can destroy your engine VERY FAST!! It will beat the bearings right out of it and can shatter pistons and even bend rods.
I don't know enough about the balance specs of the different 340 balancers but if this 360 you have was internally balanced using heavy metal (Mallory metal is what it takes, ask the balancer if this is how he did it to verify it) you need a neutral balance vibration dampener also in addition to your neutral balance converter. The 340 steel balancer could have some degree of offset balance. Again I don't know the 340 balancers well enough to say. I do know 340 steel and cast balancers are different but that's all I know. Hopefully someone will chime in and say what the differences are. It sounds like your in the right ballpark since when you changed the balancer it got better. Just need the correct balancer to get things perfect. Maybe a neutral balance Fluidamper would take care of it if you have the bucks.