Firstly, I would caution you against using mechanical methods on your soil when it's wet. Doing so will only further compact the soil and make your drainage issues worse. Clay and silt are especially susceptible to compaction.
Where I live, we have similar weather patterns to yours as far as winter rain and summer dry are concerned, except that it's wetter longer here. We also have mostly clay soils and lots of slopes, so I feel like I have some experience with what you are dealing with.
I am curious why you feel you need to drain the sloped area you are working on? What are you going to use it for? Are you planning on irrigating it in the summer?
And what is the history of that area? Has it been grassy for some time, exposed to the sun and rain with little to no organic material added to it?
The water in the swale must be coming from uphill. Water will naturally go downhil over time. It may seem like it's not draining, but it just might be. It could be that it's just not draining faster that it's getting filled up from the water coming from uphill.
Adding organic matter, and lots of it, always helps. The soil in the areas of our yard that have been lawn for some time has become compacted by the rain, turning it into hardpan. Sometimes it's so extensive that it's impossible to dig a hole in it. We've found that putting a thick layer of ground-up plant material on it, like arborist chips, season after season, has significantly improved the soil. When we have to plant where we haven't done that, we build a mound of soil (native is best) over the area and plant. Then we add a couple inches of compost and then mulch over that (being careful not to mulch near the trunk). All of the trees and shrubs we've planted like this have done really well. When planting on a slope, another good trick we've found is to do the same thing but to add some logs or firewood to the downside of the slope to hold in the soil. All of these methods help both with drainage and with improving soil moisture in dryer periods.
