A vertical climb in a 172 ?
Yes.
That, together with the tail first, vertical descent that will immediately follow, will, at least temporarily, push damp carpets a very long way down your priority list!
This is of course, best performed close to the ground, where the resulting high speed impact/fire will provide an immediate, and permanent solution.
Ps. H+S Notice: This post is for entertainment purposes only, and not intended to seriously suggest a practical cure for damp carpets.
PPs. Sorry this doesn't help, but I was just reading Part. FCL and I needed a lift.