Sounds like the problem we are experiencing in our 2000 Bonneville se. We get constant vibe/shaking at 50mph, and then same at 70-75mph, however at that speed the problem comes and goes in a repeating cycle.New tires didn't solve it. Balancing didn't help. Put new half-shafts on and replaced one tie rod.This helped but didn't eliminate the problem.Still the same frustrating problem.
I'm beginning to think this is a tranny problem although ours shifts fine.Keep me informed and I'll do the same. Brian