I was working with some side-drilled stick pearls and it's a similar
problem. The stick pearls are consistent with some wire wrapping
techniques, but I don't think briolettes would look "right." Here's
an idea - use the pinch bail and a small soldered jump ring. After
the pinch bail is in place,slide the ring down over the sides of the
bail to keep them from slipping out. Obviously, you need to carefully
size the ring so that it doesn't slide past the "pinch" part of the
bail. Then ever so gently and slightly, pull the sides of the bail
out away from the briolette, above the ring. That sould keep the ring
from working up and off.
I haven't done this, but in my mind's eye, it looks rather nice...
especially if the jump ring is more of a band. Just an out of the box
Judy in Kansas, where it was a gloriously cool weekend and my
butternut squash vines are trying to take over the world.