I was going to hire someone - or rent a pressure washer. Instead - I made a solution of 10% bleach and 90% water - kept it mild in case it dripped on our plants. I sprayed it on the roof with a small pump sprayer - let it sit a while - brushed it with a long handle brush I use to wash my camper - then hosed it off with a regular garden hose - low pressure.
All of the stains disappeared - I checked the gutters to make sure I was not washing off the shingle "grit" - I was not. One day later - the roof looks like new. I plan to go up today and do it again on the spots that I missed.
Thanks to those that gave me the bleach advice.