I think we've discussed in the past that replacement shutters from Altman come with the fiber washers. I don't see just the washers listed on their website, give them a call at 1-800-4-ALTMAN. I've always found them helpful.
Or do a search on this site: WashersUSA. Gotta love a company that does exactly what it's name is!
I've got about 9 360Q's on my work table right now that are going through a complete refurbishing and I'm also going to need some washers. I plan on buying them from either Norcostco or BMI Supply. Good luck! Remember to use all aluminum rivets!