Simply stated...
After struggling mightily with the problem, using a variety of cleaning products, I tried someone's recommendation and used Simple Green. I'm convinced. It did a pretty damn good job. There are still some faint stains on deck, but I'll come back at them with non-skid deck cleaner, or a power washer. But for now, SG did the trick. Good luck. (And don't forget to rig some kind of preventive mechanism, or you'll be cleaning bird crap again, and again, and again...)