This really helps, Stuart; thanks!
Yes, what I am seeking is not just "more" padding, but that extra diameter as well. Spot on! If two or three layers of tape will get me closer to what I need, then that's surely the way to go.
You're absolutely correct about contact area and pressure. With just the present single layer of tape, it makes my teeth itch* after awhile.
Best,
Dan. (*whose teeth don't actually itch, but feels the old phrase neatly describes the niggling sensation after holding the 'bars for 16 hours)