Any ideas on wooden drip rails?

I need to install some drip rails over the doors of my wooden tear. My doors have no seals- just wood closing on wood. Water seems to gather at bottom of doors and swell the wood. Not enough room to install foam seals between door and sidewalls (have tried the thinnest stuff made). The aluminum ones that are sold would not look good. Anyone have any ideas on how to build drip rails from wood? I am thinking:
-cut pieces out of oak planks, attach them together
-rout out one side of the rails to channel the water
- stain them to match birch sidewalls on tear
-spar the heck out of them where the water would go.
- glue and screw them to sidewalls
- seal the edges where it attaches to sidewall
Think this would work? Any better ideas? How far should rail be from the door? How far should it extend?
thanks
-cut pieces out of oak planks, attach them together
-rout out one side of the rails to channel the water
- stain them to match birch sidewalls on tear
-spar the heck out of them where the water would go.
- glue and screw them to sidewalls
- seal the edges where it attaches to sidewall
Think this would work? Any better ideas? How far should rail be from the door? How far should it extend?
thanks