. . . This "shell" slides into a holder that the bead
strings funnel through. How can I remove this Lucite "shell"
without damaging the piece so that I can run the bead cord through
If the “shell” and the “holder” would not be damaged, you might try
soaking it in vinegar to release the adhesive. Perhaps check with
your friend about trying a drop or two of vinegar at the junction of
the two materials on the back of the piece to check for both adhesive
softening and for damage to materials.
Judging from the image you listed with your first post, the "holder"
seems to have holes at the side for the original stringing. If the
adhesive cannot be safely removed, you might drill through the shell
so that you can simply string through the piece. Use a slow speed to
avoid either burning or cracking the plastic.