This is what I got at the end.
Fweeee! The beginning of a round braid of six thongs.
Once I got the wrap on the stems, it then became clear I'd need to undo some of that braiding.  **SIGH**
I tied each braid off TWICE 1/4" apart with waxed thread, using surgeon's knots.  I damn sure didn't want these things coming unthreaded.  That would be... bad.