If I were attempting to save this plant, I would remove ALL the leaves and carefully all the brown bracts on the remaining BBs and then soak for about an hour. Then I would place it in a 1 quart Zip Lok bag filled with the equivalent of a 3" pot of well soaked but drained orchid mix of preference. (I use small fir bark and perlite). Bury BBs, as a connected clump in this case, about 1/3 of their length in an upright position and seal the bag. Place in a warm place in the house with light but no direct sun on the bag.
In this way, a miniature greenhouse has been made. The new growths should start elongating and form roots with the increased humidity. When you pot out, use a finer bark than I suspect you have been using and again bury the BBs about 1/2 to 1/2 of their length.
Next time when removing rotten roots, and there are no viable roots on a piece, do not remove the entire root but only strip the mushy outer velumin from the root itself. That way, you will have "a string" to help anchor the plant but no rotten "stuff" to muck up the new mix.
I agree with White Rabbit in placing this plant outside for the summer when you have roots. Practicing on unk. hybrids and being successful, makes you more confident when you encounter a really nice plant that gets into trouble!
Good Luck,
CL