Hey Rance,..artillery fungus is tough. It's one of the things to look for when looking at any house wash. Another thing is cracked or broken windows. I then inform the customer they will not come off and will be there when we're done.
Anyhow,..don't waste money on detergents, acids,..etc,.. the only way to remove these with 100% success is a Magic Eraser. It's alot of work but it's not hard,..although we don't provide that service I think it could be marketed as a niche' service.
I've seen so many people over the years claim they has something that worked,..they would claim to have something that worked,..and then say "You still have to Use Some Elbow Grease",...Skip the miracle cleaner and use the magic eraser and elbow grease.
On oxidized siding you're going to leave little shiny spots where they were rubbed off,..but they will come together over a time. Will not work on soffit or ceilings,..too much give to get any pressure on your scrubber. We will sometimes remove a few in porch areas, or other very noticeable areas,..but if there are alot we don't even bother.
Knowing what they are and having an abundance of information on the problem gives you alot of credibility with the homeowner,.they like to hear that you understand the problem and just aren't standing there saying,.."I don't know what they are,..I know I can't remove them though"
Edit: I buy magic eraser generics on ebay,..I get 100 of them for 25.00. They are the same size or close to the Mr. Clean brand. We use them for lots of things,..toe kick marks on doors, places where lawn mower handle rubs against siding,..etc... We keep a 5 gallon bucket full in the van.
Jeff