i stabilize it by placing the bottle in the cage as in this piccy
when boiling the bottle the cage arm rests on the cup for support, hope this helps.
Tried the bottle in the cage, works best when the bottle is full, the second tip is something I'd not picked up on, thanks I will try it sometime.
The thing that used to irritate me with them was that it rattled a lot when packed but I found by pushing the top retaining wire all the way over the top it's a lot better.
I recently also found that the vent holes top and bottom line up almost exactly with the underside loops of a Snugpak response pak, which, with the addition of a couple of mini carabinas, make it into a handy little outing bag including brew kit.