Valerie, don't worry about going off topic. It's ok.
You could make something like a baby sling, where there's a bodysuit harness (for the beardie) attached to a neck strap (for you) of some sorts. This way she won't fear falling off of you and you won't have to keep one hand on her body or remember to lean back while doing something.
Perhaps Sizzle isn't a bunny lover? They do have preferences over what type of stuffy they want to snuggle up to. Take MoMo for example. For her birthday, I gave her a light green stuffed frog and she absolutely hated it! So much so that she wouldn't even stay on the same side of the tank. Luckily I had also bought a light blue puppy, made of the same material and same shape, and gave that to her. Well, I had never seen anyone fall in love with a stuffy so fast in my life! That puppy became her protector, just like how Mr. Bear was for Pookie. So, in summary, you have to try different types of animals and the materials they're made out of until you find that perfect one. This also means that you'll end up with ALOT of extra stuffies on hand :wink:
Unfortunately, MoMo decided to go back into her cave today. Boo hoo hoo!