Solution for rainwater diversion

[Kris L.]

I have an interesting issue.  I have a 3:12 sloped roof that abuts a nearly flat patio roof.  If the wind blows from a certain direction, it allows water to intrude into my patio ceiling.  If I could install a gutter on the slopes roof, I could eliminate most of the water from the area, but I only gave about 2.5-3” of space between the shingles on the slopes roof and the patio roof.  Shallowest gutters i have seen are 4”.  Does anyone have a clever solution?

PS:  This is in Florida, so bonus points if you know of something that can take some serious wind.