"(...) my hand categorically rejects two button mice â" the dangling ring finger causes me genuine physical discomfort (...)"
I recently noticed that a colleague that suffers from RSI and was in the process of trying different mouses holds his mouse different from what I do; I hold keep my ring finger and little finger both on the right side of the mouse, either stacked on top of each other or with both fingertips touching the desk surface. Mouse movement is controlled only using the thumb and the ring finger; the rest of my hand is normally not touching the mouse except for my finger tips. Forefinger controls the left mouse button, middle finger controls the right mouse button and the middle button/scroll wheel can be controlled by both fingers. I've always held my house that way and being a long time X-user, I have always used 3-button mice.
Having noticed that difference, I tried holding my mouse the way my colleague did: one finger for each button. This causes major strain in my hand (exactly the place where my colleague had troubles), probably because my fingers have different lengths. So I went around the office, asking people how the held their mouse and whether they had complaints. Turns out, most people held their mice in a way similar to how I do it. Those that didn't had more trouble with their hands.
I'm not saying you should switch hand-on-mouse position; everybody's different. However, you might want give it a try.