Does water sheet off of the roof, and fall a considerable distance onto the planting area, or is this roof runoff more indirect?

More indirect. The water is channeled into our rainbarrel, and any overflow (of which there's usually plenty) falls to the ground from about 4 feet and then runs downhill, paralleling the driveway.

So there is not significant pitting or erosion from the runoff; that makes plant recommendations practical.

I don't think plants alone will control much of that sporadic, intense runoff. Modern designs here in Portland all use swales, requiring some excavation.

Potentilla shrubs would survive everything you mention. Not sure what their growth habit would be in "open" shade (instead of deep shade under trees).

Overflow from a single source like a rain barrel is handled by many homeowners with those large black flexible tubes, but of course you have to have a suitable destination downhill.

Luzula sylvatica

Gravel in the ditch doesn't necessarily make it drain better. It means you have a ditch with gravel in it. For instance, you can't make a puddle drain faster by filling it with gravel. In your case, the gravel is slowing down the drainage. Rake it back up on the shoulder or driveway. It isn't doing any good in the ditch.
I wish I could help you out on your problem. :-(
Maybe a picture or two would help? From the rain barrel looking down the ditch, or the other way. And one showing the shade and cause of it.
Mike

How wide is this 'stretch of ground'? Can you make a vernal pond?
I have several that are dry during the summer. I made the bottom smooth so I can mow them when needed or I use a string trimmer. I didn't plant the grass, it just grew by itself. It's underwater for about eight months a year.
{{gwi:2128688}}
You can see the shoreline on the far side where it meets the hardy Geraniums.
Mike

great treatment below

Here is a link that might be useful: lots of advice and plant lists here