Sometimes the answer is "quit working, go home, and ask your sweetie".
My partner is a genius and had a very straightforward solution: get rid of the imagemap and replace it with some absolutely-positioned links that use regular anchor tags. Not only does this solve the problem in a lightbox-friendly way, it also improves accessibility -- the links are now text with a font-size of zero: usable for a screen-reader and invisible to others.
Simple demo here: http://www6.wittenberg.edu/lib/testbed/imagemap/
Tomorrow perhaps I'll write a little script to convert my image maps to absolutely positioned elements for the more complex real-life image maps.