Here's an update to the thread. The owner got an elevator company in to check it and it turns out the control cable in the shaft was shorting intermittently. I wouldn't have found this in a million hours, so I guess it's a good idea to bow out when you feel over your head sometimes
May that have caused the contactor to chatter? The cable being damaged should not had caused and over current condition in order to blow the fuse because you indicated that the fuse was in series with the coil. As such the damaged cable may have interfered with energizing the coil.
If the control circuit was intermittent and causing the coil to chatter resulting in blow fuses, I would suspect that the contacts of the contactor have been stressed to the point on almost being welded.