I took a Dremel tool and carefully ground a fairly uniform surface onto the screw, and then I drilled a hole into it. I was very careful to keep the hole in the center, not make it too big, and not make it too deep.
Then I took my chances with a small easy-out type screw removal tool. As tight as the screw had been when I'd broken it, I wasn't confident that I could remove the screw this way. But before I put too much torque on it, I realized that the pin was off-center, as mentioned on the previous page. Once I pushed the pin back into place, the screw turned out very easily.
While it was a hassle that I wish I would have avoided (and could have, if I'd been paying attention), it's good that I replaced the screw, because it was so worn. In the photo above, you can see the concavity worn into it from much use of the lever over the years. The "easy-out" is still in the screw, and the screw head is lying nearby, upside-down.