Just a quick interim update while I'm waiting on my backdrop to arrive.
I set-up my Doug Baldwin lights very close to the beads for these next few photos, plus I put a piece of rigid white poster board both behind and balanced on top (across the top) of the 2 lights. It seems to be much better, although there was still a significant amount of editing I had to do in Lightroom to lighten up the pics. It's a work in progress...