Bob,
There's a more then average porbability that drive train vibrations could be both transmitted through the Healey's substructure, and even amplified by it, to give what we commonly refer to as scuttle shake. It happens that the brake drums were the unaddress and undescussed item that turned out to be a major contributor and that surprise discovery took the lions share of attention away from any other possibility.
Also, Steve Byers mentioned his efforts to reinforce the transmission tunnel opening in the fire wall and, back then, it was thought that that weak structure was the cause of scuttle shake. Martin Jansen mentioned the issue of rear wheel tracking, which he indicated would be improved by moving the front spring mounts 1/2" toward the center of the car, as a cause of scuttle shake. And, I can go on with other possibilities.
So, what is your pleasure? I have owned my Healey since new and have driven it throughout the country (i.e. "Route 66" like). I met my wife 2 years later and it was our first family car with my wife doing most of the Healey driving. I also took my Son home from the Hospital in a basonette on the folded down back shelf with top up (imagine doing that today). So, when I drive my Healey with the Beach Boys blasting through my sound system, a little shake does not deminish my youth regression.
And yes, I made a fixture that allowed me to have my wheels tires and drums spin balanced as a unit. However, although it worked quite well, the wheel and tire must be mounted in the exact same position with respect to the drum. That is why I would not recommend that approach to others.
However, when I completed rebuilding my Healey in 1989 or so, I had the wheels and tires spin balanced and the car was tight and solid at all speeds...NO Shake. It was over 10 years later that the car seemed to exhibit any shake and, from what Patrick posted, it probably was due to substructure beginning to relax.
Just my thoughts,
Ray(64BJ8P1)