Hmmmmmmm, it surely do look like rust to me. I've no idea what to suggest to you - I don't have anything to go by as an example since none of my guns, old and very old, have ever looked like that at any time.
I'd be grateful if you would allow me to post that image on muzzleloadingforum.com, where about a 1/4 million BP shooters might have a better idea of what to do.