Don:
If it were mine, I would send it to TAG-Heuer for an overhaul / restoration. It will be a shade expensive, but I beleive that you will be blown away with what they can do with these old guys. The only limiting factors are the dial and bezel; other than those elements, it can come back looking like new.
The other choice is a local watchmaker, but you would need to be confident in his / her level of skill (and supply of parts). If someone wants to put this big guy on a polishing wheel, you should be certain that they know what they are doing.
EXCELLENT QUESTION -- on that subject, other than TAG-Heuer, and their retired man (Hans), does anyone else have a favorite source for service on their chronographs??
Good luck with this Autavia and let us know where you go and how it works out.
Jeff