Mike E. Fullerton wrote:

I have never encountered this problem in any other house I have lived
in. How to best fix this? Someone suggested putting a strip of plastic
vapor barrier between the hanger and the duct to allow slippage.
Couldn't that be a fire hazard?

Buy the cheapest, thinnest car floor mats you can get that don't have any
carpeting on them. Cut them into strips wide enough to do the job. Or,
maybe strips of felt. Or, screw the hanger straps to the duct with
self-drilling screws.

But before you do that, can you SEE it happen? Maybe it's not what you
think.