This worked, but it was difficult to find the right balance of magnetic force versus freedom to slide. Too many magnets caused friction to interfere with positioning; too few allowed the mouse to occasionally fall during rapid use. I suspect that magnetic ball bearings may be required to simultaneously permit sufficient upward attraction and freedom of lateral motion.
I next tried an inverted touchpad fashioned from an iPod Touch running Logitech's Touch Mouse software:
It was difficult at first to get used to the inverted tracking behavior, but I learned to love this arrangement. I ended up using it for three months, only to stop when I moved on to new work and the Touch had to stay behind.