Ongoing vibration issue

Sounds to me like you're fighting a balance issue.
You don't say what balance your 408 was built for (internal/external), or what your previous 340 was, either (they were built both ways, depending upon year- so you could still be fighting the identical issue).
Replacing the torque convertor/flexplate will not accomplish anything unless they are replaced with the proper units, ie throwing a brand new neutral balance TC on it when the engine requires an external balance... An incorrect harmonic balancer could also be contributing to the issue for the same reasons.
Please elaborate on your build and what parts you used, in addition to how you had your rotating assembly balanced.