Bedrock drainage help

I have an area behind my house and driveway that is bedrock. It is about 60' long and 3' wide. The builder of my house didn't install a swale on the hillside behind my house so all of the surface water runoff hits this bedrock.

The Rock has a very slight grade so it drains to a ditch alongside my tar and chip driveway. However, there is still about an inch of water that doesn't drain. It is an eyesore.

I need it to drain better and provide a better slope for it. I would also like to capture the water and pipe it down the driveway. I can't keep the current ditch free of debris and it keeps eroding my tar and chip driveway.

Should I cut a trench into the Rock and install a French drain or install a retaining wall with a French drain? I'm open to any diy solutions.

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