If your toadstool is large (and it sounds like it is), IMO you'll want it to attach to your rock work. It'll be a little top heavy when it's fully open, at least enough that a medium size crab or snail can push it over if it's not attached. If you're worried about it attaching too much to your rocks (it'll attach anywhere on the stalk that's touching rock), you can make a sleeve out of PVC pipe and slide it over the stalk, limiting the toadstool's attachment to the rock only at the base.
I'm not sure about the toothpick and rubberband method you're suggesting, so I can't say how well that would work.
When we bought ours, it took about 3 or 4 days to get adjusted to our tank enough that it had polyps out most of the time. It shed constantly for the first 6 weeks we had it, but rarely sheds anymore. It seems very happy now, as long as water conditions remain good and stable. I've even cut a couple of frags off of it with no ill effects. In fact, it's been a month since I fragged it and you can't even tell where I cut off the frags.