And so, here's how it went:
The master cylinder was leaking a little fluid past the rubber boot at the bottom. It also wouldn't stay bled - go figure.
This is the piston kit for rebuilding the master cylinder. It's a lot cheaper than a new cylinder, so if the cylinder itself is in good shape, you can go this route.
The first order of business is to drain the reservoir. A turkey baster works well for that, or you can unscrew the reservoir and pour the fluid out. Then remove the reservoir tube and the brake line from the master cylinder. Be sure to protect the paint around the area from the brake fluid.
This is the end of the master cylinder, with the plunger still held in with a snap ring. You need a pair of snap ring pliers to remove the snap ring.
Here are the parts as they came out of the master cylinder.
In this case, the master cylinder bore was in great shape, so I cleaned the little bit of gunk out. This is an aluminum cylinder, so there's not a lot you can do if the cylinder is scarred or scuffed. You could try to polish it up, but it's less likely that you will get a leak-free assembly than if this was a steel or iron cylinder.
This is the grease I used to lubricate the new piston seals. This is DuPont Krytox GPL206 fluorinated grease - basically teflon particles in a fluorinated oil. This grease is stable across a huge temperature range, and it does not react with brake fluid at all.
Putting the master cylinder back together is very straightforward. The piston and seal set go into the bore easily, and the snap ring seats without much of a fight.
Don't forget to put the new rubber boot on the plunger before putting the rearset hardware back together.
Finally, bleed the system however you prefer. I've had good success with both the reverse bleed method, and the conventional bleeding from the reservoir through the calipers.