Well, I think it's a success. It was a bit frustrating at times.
So here's the way I approached the repair:
First I let down the mainspring, removed the gas chamber, spring, and connecting parts and set them aside.
Then removed the dial, bezel and motion works. I could wiggle the dial and bezel out around the hands, so just left them in place.
Then the front plate came off, and the wheels were removed, then took apart the mainspring barrel.
Found the hook that was broken, and brazed it back in place.
Oiled the mainspring, and put the barrel back together.
Put the winding arbor back in place and tested it. All fine so far. Reassembled the main parts and oiled the pivots.
Now the fun part. The spring that the gas chamber manipulates has to be compressed and held in place at the same time the winding arbor is tensioned and held in place, and at the same time the chain is manipulated through the hole, put on the pulleys and locked in place with a little pin.
Whew! You need at least 6 hands! So here's how I approached it. First I compressed the spring and held it in place with two zip ties. Then I tensioned the chain, making sure it was on the pulleys, pulled it tight through the plate and held it in place with a push pin through a link in the chain. Now I could wiggle the end of the chain through the brass plate that the gas chamber pushes against, and hold the end link with a pair of forceps. Now I was able to cut the ties, letting the spring push against the plate and the forceps. With that part tensioned, I put the little pin through the second link (that's where it was when taken apart), letting it hold the tension from the spring as I removed the push pin and the forceps. Whew! Now I was ready to test the winding mechanism. I gave the spring part a push and watched the clock wind correctly. Three more pushes, and back together it all went.
Fun! But nothing requiring a doctorate in mechanical engineering

I'm including some pictures of the progress. Enjoy - and I hope they help if you try it yourself! They are not in order, but if you note the picture names you'll figure it out. The clock is running in my shop right now, and I'll have to make sure it continues running and regulate the time.