This clock has a "Type A" barrel assembly according to the information at sangamoclocks.com. The mainspring bridle had been "modified" to slip like an automatic watch, which destroyed the sleeve screw (part E in the diagrams at the site above) by shearing off the tip, leaving the clock to wind at full speed forever, which makes it unusably noisy and prone to serious wear. I think a previous repairer just didn't understand how the winding system was supposed to work.
That page linked above (which was a huge help!) recommends modifying the whole setup to be more like "Type B" if you have a broken sleeve screw, but I just fixed the screw instead. Plan B would have been to make a new screw, but that would be more work. The original screw was blued steel (left blue) and drilled easily. I used a piece of pivot wire, left full diameter. It was a good tight fit but I used a dab of blue loctite anyway.
The finished repair. Now after some adjustment, the clock winds the spring most of the way and then the brake stops the winding motor. As it runs, the brake lets the winding motor slip just a bit periodically, maintaining the wind at the setpoint. If power is lost, the clock will run for many hours on the stored energy in the mainspring, and then wind back up to the setpoint when power comes back. It's a great design for the unreliable power of the 1920s.