Well, today I received the BHP that I had ordered from Speaker City last week, and, this evening, I had a go at the TVC modification that Ray Bronk so kindly descibed in this thread about a month ago. And I am pleased to report that I did not incur any discernible damage to my TVC in the process!
The changes in the sound of the TVC brought about by the BHP damping mod are subtle but important. The sound is now more natural, relaxed and composed. By comparison, before the mod, the TVC could sound a bit "high strung" and a just a touch "ragged around the edges" in difficult peak passages. I believe there is also now less of a tendency for the treble frequencies to become strident on recordings that tend toward brightness.
All in all a very successful tweak for a non-techie like me.

Ray, thanks so much for your detailed instructions without which I would not have known where to start!
As a point of reference, I am currently at 200 hours of run-in and counting...