Thanks for your suggestions on the cause of my popping beads. I laughed when I read Robin's statement that "you can try couching down the popped up places, although generally that will make the beads pop up somewhere else," for that is exactly what happened with my circles! After finishing that area, I held the piece up to admire my work. "Wait!" I exclaimed, "what's that bead doing popping up there - and there! I'd better fix those right away!"
I started carefully couching the popping beads, only to find new poppers. After going round and round (and using more thread to couch than I had on the entire piece!), I flung the piece down in disgust. Seeking to reassure me, my husband cheerfully examined the piece: "Oh, you mean theses straight ones? They don't look too bad. Most people wouldn't really notice them."
"What straight beads?" I gasped. I'd never noticed the cockeyed bugle beads! At that point, I put the piece on the table and looked at it every now and then. I continued to play with beads and fiber making little dotee-like dolls. I ordered some beads I thought might go well with the piece. I dug out the camera and recharged the batteries. I went out and took pictures of the few trees that were still colorful and brought some beautiful leaves home and scanned them. I compared the colors to the ones in my project. Finally (almost four weeks later), I did what I knew I needed to do all along: seek expert advice...
Thanks for the suggestions, everyone! Marty's suggestion about the backing shrinking as you stitch is probably the culprit! Having a needlepoint background (no quilting), I'd never thought of that. Also, I used a relatively lightweight interfacing on the back, rather that Lacy's or Timtex - much easier to distort. I can also see how I crowded the beads between the bugle beads and the oval bead. I will probably rip that area out and try again.
Thanks again everyone! And Happy Holidays to all!