I can find a maintenance kit online at ereplacementparts.com for $67.26 (Service Pack 1617000426), plus shipping (so $75). It comes with the necessary gasket (plus more), and a tube of grease. Plus replacement bolts.
It also has a diagram showing all the parts.
The ones marked in black are the parts in the service pack.
We put down cardboard as a surface to work on.
Once they are removed, we can pull the bottom (unpainted) part off the rest, revealing a spring and the broken gasket.
Putting that aside, we continue to disassemble things, by removing the hex-head bolts. A 3/8 hex key wrench works for them.
And once they are removed, it is possible to crack the paint and separate the top and bottom halves.
And pulling them apart reveals the main piston cylinder.
and then just put everything back together, with the new bolts and gaskets.
At this point, there is grease everywhere, and I can't really take more pictures. But it seems like just taking off the bolts, greasing things, new gaskets, and then putting it all back together in reverse, with the new bolts.
Update: After getting it back together, I tried to run it. The motor would start, and then immediately freeze. Taking it apart again was exceptionally difficult. It appears that the end of the piston had come off the cam, and then the cam had rotated until it jammed.
I took it apart and put it back together several times, with the same result. So finally I took all the pieces to Austin Tool, and the guys there showed me that the piston is not symmetric -- it is a little bigger on one side (right) than on the other (left). If the bigger piece is next to the cam, the piston is a bit too far over and comes off. If the smaller side is next to the cam, the piston is closer to the cam and stays on. And with that small difference, it works.
I used it for two days, and the bottom gasket broke. Again. I plotted out the maximal gasket -- it should be round, with an inside diameter of 2 inches and an outside diameter of 3 inches. Rubber, about 1/8 inch thick. It appears to be difficult to find such a simple gasket.