I had been power washing the junk off but you really are not supposed to do that because it knocks off the granules that are necessary to shingle longevity.
Luckily I have a roofer as a neighbor and I was discussing this problem with him. He said just have zinc strips installed. This was completely new to me. He told me where to get them and I asked if I bought them if I could pay him to install them. He agreed.
It seems tiny amounts of zinc leech from the strips with rainfall and algae can not tolerate zinc. My problem is solved, thanks to a knowledgeable neighbor. One strip along the top row on shingles, that is it!
Thought you might want to know. Ken