Ideas to stop leaks?

[Ridgerunner]

Instead of putting a drop at each channel I'd run a bead across the top of that piece. Wet your fingertip in water and run it along the bead to make it concave. That seals it well and to me is more attractive that a round bead.

 

[aart]

With practically no overhang

Good Catch!
I'd observe that eave during a good rain.