Yeah I used Plastidip on the mast a couple years ago. Wrapped the disintegrating rubber part tightly with 12 lb test monofiliment to hold everything together and then dipped three coats. Worked great.
Not sure I'd do that with the base though. If I go to the trouble of R&R-ing the base - even if Dub's right and you don't have to completely remove the headliner, (and I'm sure he is) I'd want to replace with something new.
On the other hand if there's no reasonably priced alternative, PlastiDip to the rescue! Wonder if you could make a mold and create a new base plinth entirely out of PlastiDip...?
Really, does it matter what it looks like? How many people are tall enough to see it anyway? I say the h3ll with the truckers - cut a base plinth out of marine plywood, and paint it black!