John,
If there is grease on the shingles you can use a sodium hydroxide based cleaner.You have to be detailed in the rinse (i.e. every square inch with no more that 500psi. There are numerous roof cleaners on the market that contain Sodium hydroxide,I prefer the spped and easy of chlorine,but it will not have any effect on the grease.
Judging by the pics you posted most of the work can be done with and extention wand.