I wasn't thinking when I posted my question. When the CB is up, you can of course measure the thickness from below with the boat on the trailer (at least to the degree that the thickness of the "head" is a constant, as you can access the forward face of that part of the CB).
So, I just measured it an the result is an annoying 7/8" (smaller than minimal size for onlinemetals).
Near the handle, the head may be slightly thicker, but I doubt it would be a full 1/8".
Still like your idea of suggesting this to Rudy.