Based on Sam's advice, I loosened the G string until there was just enough tension left on the string to keep the ball end from jumping out of the bridge. Then I attacked the tuner, removing the large screw that holds the gear to the back of the string post.
With the screw off, I removed the gear, exposing the leaf spring that tensions the tuner. Pulling the string post down through the headstock about half-way gave enough clearance to remove the spring, which turns out to be made of two pieces- a black plastic shim, and the chrome spring:
I took the spring, and tensioned it by bending the end up slightly:
It doesn't take much of a bend to produce the required tension:
Then, I reinstalled the spring, checking to confirm that I had sufficient tension:
After re-installing the gear and tightening the screw, I made sure to hold the string with my thumb as I tightened it up, to keep the string wound neatly around the post:
After repeating the process four more times, I was pleased to find that tuning is now much smoother. Best of all, after fixing the loose tuners, the dead spot was considerably reduced. Before re-tensioning the tuners, I had a broad dead spot from about B to D# on the first and second strings. Now it only affects the D# on the first string.
