Try this
stuff
I had that ugly brown/back mold looking stuff on the roof of my Airstream. Put it on about 15 months ago and it took care of the job. You really don't have to scrub, just spray it on and forget about it. It has a residual effect that prevents regrowth for a period of time, too. I haven't climbed up there recently to check on it, I'll try to take a look on Sunday.
However, there are some caveats here. Mine is a '73 that has lost most of the clear coat. Sounds like you need to use it on the painted surface as well as elsewhere. Call them and discuss how you want to use it. I suspect your roof paint is a lot like automotive paint, the bottle label doesn't specifically mention automotive applications. But I suspect it will work. Call them first, their customer service people are top notch.
Jim