A few random thoughts...
If rain is heavy enough to swamp the gutters, I don't think black streaks will result from that. The residue from the roof will be very diluted and the flooding water will carry it away. Steaks result from water slowly dripping down the sides. But, It Never Rains in Southern California, so what do I know???
I think adding 2" gutters might be excessively large. Maybe 1 1/2", or even 1" pipe would be quite larger than normal RV gutters.
Interested in seeing your results, because you may be quite the craftsman. In my minds eye, I don't see how it is not going to look pretty cr@appy. But willing to give you the benefit of the doubt until the photos are posted.
The clip-on downspouts for RV's have worked very well for us, to reduced the black streaks.
Be careful ripping PVC pipe. I have done it. And I was very surprised with how much stress there was in the pipe. I have had it pop open as it was sawed, but worse than that I have had it clamp down on my table saw blade. And you won't know what it is going to do until you're in the middle of a cut. Be prepared with wedges to insert in the kerf as you go.