Hi. Those new designs are really cool looking! Now I want to get out my pieces and start fiddling that way, too.
Regarding keeping mosaics in place... It's all done with friction. I squeeze them into place. Now different designs fit better or worse depending. Most designs, even if loose, will stand up vertically just fine; gravity pulls them down, not out, but they're in tight enough that they don't have much room to budge. A few designs stay really really well, and I have pictures of a few things being upside down:
A lot of designs I don't really want to turn upside down until I'm completely done with them, on the off chance that they might not be as sturdy as I thought. It just takes patience, though, to work on it long enough to get it to fit just right.
That being said, I do know people who have used or plan to use double-sided tape for mosaics at a show, just because of the bumps of travel and potential disastrous results. But if you do it right, it will just stay. Sometimes I try to bang the slopes out on the table, and they won't come out until I pry a few loose. Then there's a great big cascade. ;-)
Gotta run now, but I can't wait to see what you come up with! ;-)
Katie