I drew a grid on an 12" x 18" piece of paper and decided we would play a game like Scrabble. I would draw a strip, and he would draw an intersecting one. Then it would be my turn, and we would continue until the page was somewhat full.
It was actually easier than I thought it would be! We completed three. I've traced off, and cleaned up, one of them. Here is it below. I've indicated the panels I drew with blue. Martin's are in green. The first strip drawn was the middle horizontal one, starting with, "What are you doing?" Click to enlarge...

I'm thinking this has the potential to be a fun challenge for cartoonists, much in the same way a "24 hour comic" is!
(Update! See our other Cross Panel Comics here.)