I had to do a major overhaul of my Century III Autopilot and found, at that time, that Century itself & Autopilot Central were the two principal places to have components overhauled ... and ... King Avionics (KS) and Muncie Aviation (IN) where two other shops known for knowing how to work on Century Autopilot systems but not doing the rebuilding of the components themselves.
I was having numerous problems with my autopilot ... Muncie did the work for me as they were the closest to me (OH) and several other pilots at a BPPP course in Columbus OH I attended spoke well of them. I would up spending a little more than twice the estimate for the repairs and I was upset with that but the autopilot (after one immediate return on their nickle) has worked well (knock on wood) since.
P.O. Box 610
Mineral Wells, TX firstname.lastname@example.org
3112 N. 74th E. Ave
Tulsa, OK email@example.com
New Century Aiport KIXD
Bill Hill at firstname.lastname@example.org
5201 North Walnut Street
Muncie, IN 47303
I hope this helps.