Thanks to Brian's wisdom, I used hose clamps, and was very happy with the result. Quick and easy and very secure.
I also recommend putting the screw clamps on the inside. Using a long screwdriver allows you to reach in *through* the holes in the ash catcher ring and tighten them down nice and snug. Oh, and don't forget to reverse the direction of the tabs on the ash catcher ring so they hook onto the hose clamps securely. And make sure your hose clamps are stainless steel (I think that's the default for hose clamps, but better safe than rusty).