Don't use a standard house paint. It will peel off in just a few months. I'm thinking that a roofing mastic would be better. Something like Sno Roof.
Power washing the roof is a great idea to remove the dirt and dust. Be careful, the roof will be slippery.
Spraying is a good method for application. Plan on two coats from two different directions or sides. It will be difficult to get all edges at one time. Using a lift is optional if the roof can support your weight.
Spraying a mastic coating will require a powerful gas powered airless sprayer, a large tip (min. 525) and 3/8 inch airless hose.