Even with all the precautions, wax on the screw etc. I've had a few break off. I've basically routed them out with a dental burr on a dremel which worked but was tedious. I was at a hobby shop this weekend and got some solid and hollow brass tubing in various sizes. Turns out a 3/32 I.D. hollow tube is a tight fit around both Waverly and regular tuner screws. I put a solid 3/32 rod inside so I could chuck it up on the drill. Beveled the end on the belt sander to sharpen it. Over drilling the screw in REVERSE grabbed it every time and extracted it. The hole left was covered by both the Waverly plate and the conventional closed gear tab.
I originally thought I'd drill clockwise and use it like a hollow mill but that grabbed the screw and just pushed it deeper. You could hollow mill it out with a larger I.D. tube but that would leave too big a hole and would not be covered by the plate. Going in reverse worked like a charm. I did 4 or 5 screws and they all came out easy. Have yet to try it on a real guitar but it should work.
The Problem
The Tool
The result
The resulting hole is covered by the tuner tab or the open geared tuner plate