Problem Solved!

Well, I only got one suggestion for cleaning my cookie sheets and decided to give it a shot.

I made a paste of baking soda and hydrogen peroxide and smeared it over the offending cookies sheets. I was supposed to let it sit for two hours but I fell asleep, so it was left overnight. This morning I rinsed off the pans, gave one or two spots a bit of a scrub with a nylon pad, and there you are. Worked like a charm.

Almost as good as new!