Tube microphonics have never been enough of a bother for me to try dampers, but that could work. In my experience it usually happens more when the amp is first powered up; once the amp have been left on for a while the tubes have warmed up and don't "pop" anymore.
Cleaning the pins of tubes is a good idea if they're dirty, only because it improves contact. A dirty tube can produce buzzing or other static noise. Clean tubes will settle just as much however, it's just natural as far as I know.
An experiment: try gently tapping one of the tubes with your fingernail (don't contact it with your skin or you may burn yourself). If the sound is remotely similar to what you've been hearing, then it's the microphonics of the tubes. Don't worry, tapping the tubes or bumping the amp chassis wont hurt them. Just don't hurt yourself!
Edited by MuppetFace - 1/20/13 at 3:08am