I have tried the grease and it doesn't take care of the problem. It seems to have MAYBE made it a little better (but this is probably in my head).

Any other suggestions?

What about taking apart the door? Maybe taking off the inner door panel. I've never had it off on this car and don't know what it exposes.

It seems like this is a fairly common problem. Has anyone ever contacted Honda about it?

Thanks for everyone's help so far.