Thank you Gonzo for your advice above.
It just so happens when I drove my car on the highway the first time after reinstalling my balanced drums the other day, I did pull over into a rest stop to perform a simple check of touching my rear drums to determine what temperature both were at. But at that time, I was more concerned to see if I adjusted the brake shoes equally on both sides prior to putting the drums back on. A long while back, I once discovered one side was a little hotter than the other and therefore, I made the necessary adjustments to my drums. But please read on...
Today, in following your advice more closely, I decided to take the Healey on the highway again, maintaining a steady speed of 55-60 mph for a couple of miles, the speed range sufficient to cause that rumbling and slight gyration to steadily occur. Then, I gradually pulled over and stopped into a rest area to observe what's going on with all "four" brakes, not just the rear drums.
My observation was, with both front disc rotors, I was barely able to keep my finger touching the disc rotors. Both were equally high in temperature (not flaming hot, of course, but assuming operating normal due to friction) . With the rear brake drums, both were equally cool to the touch.
Normal?
Assuming for the moment the front discs are functioning normal and not so for the rear drums, then lets assume an adjustment is needed for the rear brake shoes only, and nothing else. I know that to adjust the rear brake shoes, one would adjust the tappet adjusters in order to expand the wedge adjusters, enough until one can hear the drum just slightly touching the shoes after manually rotating by hand. Is this standard and correct? If so, then I have a kicker issue, maybe. I noticed when I rotated the drums, I felt a slight snag occurring at one point only along a 360 degree manual rotation. This is occurring on both sides. Why this slight snag of the drum rubbing against the shoes? And any other thoughts or opinions as to the cause of this slight ongoing rumbling and gyration?
I am still waiting for my 2nd set of drums to be balanced and make a further study/comparison. But as I remembered, that slight snag also occurred when I installed them new from the manufacturer. Still, it will be interesting to learn the results of that. I will post my results when the 2nd set are balanced and installed.
Thanks for any input on this subject.
Paul
PS - In any event, the car rides better than it ever did.