The small rings are a problem and will cause binding regardless of what tool you use or how slow you go. Fortunately, there aren't many of them that are small. I like to leave the bottom open and put a base of nice material there rather than a ring.
Several folks have suggested double sticky tape and I'll give that a try. I currently use screws with wide washers on each side and bring up the tail stock with a flat piece in the middle. Never had any problem with things moving around. And now that I've decided to sharpen my parting tool, I think I'll be just fine.
May be a couple of days before I get to ring cutting. Today the big blank should be glued and dried, so I'll be re sawing, and we all know how much fun that is. I've found that these bowls need to have the re saw process done BEFORE you do your design. I need to know how many pieces of re sawn wood I have to work with before I try to design something. So that's today's goal
Thanks for all the advice, and as this thing comes together, I'll post pictures.