After much searching I think I'm going to have to settle for a dino juice-based grease. The only natural thing I could find was a lanolin and beeswax paste made for lubricating slide trombones :-( It didn't look like it would make my pedals or wheel bearings very happy.
So this weekend I'm going to head down to the local marine supply store and pick up some good ol' Lubrimatic boat trailer wheel bearing grease. I read all about the various bike-specific greases, but I'm still not convinced that they're any better (or different) than Lubrimatic.