I've read a lot about swales and am still confused by them.
A swale, by definition is a ditch dug on the contour, meaning that it is level all across the slope, and the mound below it on the slope is the loose excavated material from the ditch. If the water is moving in the ditch, then it is technically not a swale, it's a drainage ditch. Think of the land directly below the mound on the downhill side of the swale to be a dam, and the ditch is a pond. You need to have places that are not mounded, so that if the swale fills above the ditch to the level of the base of the mound, that it does not wash away the loose excavated material that is mounded up on the downhill side. These places are called spillways. Sometimes these spillways are armored with stone so that when the spillway is spilling over, it doesn't erode. It is usual practice to have another swale in line downslope so that the water from the spillway is captured in the next swale downslope. A swale acts basically like a long pond that is designed less to hold standing water for a long time (like a regular pond) and more to infiltrate water into the slope's surface, and thus sub irrigate the land downslope from it. It is also designed to grow trees, and shrubs, which are placed either on the mound, or on the downhill side of the mound (or in really super dry areas with fast draining soils, in the ditch). A swale system has to be super well designed if it is not going to have stabilizing perennial plant systems, as these are eventually going to hold the whole landscape system together.
Would using the leftover wood and root balls to create ridges like the purple lines on my drawing work? The purpose of this would be to slow the water draining.
Yes. To give another way of looking at it, a drainage ditch is always off contour, even slightly and that is how the water flows instead of infiltrating. If you have a log pointing downhill, in any degree at all, it will allow water to flow along it, acting as a drainage ditch. A series of logs laid across the slope, as I think you are indicating, will have a similar effect as a swale (acting as little dams and slowing the overland flow of water, and having some of it infiltrate) as you guessed and as Zach confirmed. Lay out the logs so that there are spillway gaps between them, so that they do not build up too much water and then end up moving in a huge rain event. On steeper slopes, you can also drive small stakes on the downhill side of the logs to stabilize them in the short term. plant stuff on either side of the logs. There is a permacultural saying about water catchment that says to slow it down, spread it out, and sink it in. That is the goal. That is what a swale does, and what a log across the slope does. A single rye, clover, or timothy plant will act as a micro version of this as well. Every plant, rock, log, or root cluster that is on there is going to slow water, particularly if logs are laid, like swales, across the slope. The more long term you water storage landscaping is in place, the better. So I wouldn't necessarilly flatten the land out in the end, unless you have some reason/plan to do so. You do not have to dig swales, you can just use your debris which will eventually create small rotted longish mounds across the slope.
I hope that clarifies what a swale is. :) I think you already knew deep down, since you mentioned how you wanted to place the logs. Your permie brain is working great!
I have wild raspberries growing in dense but small patches in my grassland. They are not going to be easy to keep away in a bare and recovering area. Having net roots, they are good at doing the job of soil stability, and they are tasty. Sometimes it's better to let nature do it's trick, but they are difficult to walk in. Roses can do the same type of thing and have tasty rose hips, but are also thorny and a pain to deal with sometimes. But allow them later as your system develops and they will not be able to take over all the niches. They will just be in small beautiful groves.
If you are looking to create a natural meadow where this logging landing was, then I would start with the grassland plan that Travis laid out, and lay out the logs as you were thinking. It will get things at least partially stable on the surface. After you have the grassland with nitrogen fixers also in place, you can broadcast a wildflower mix. Don't expect all the seed to germinate and produce flowering plants the first year. You may have to do it several years in a row depending on the impacted soils you are dealing with.
You can cover stumps, logs, and roots, with heaps of sticks, leaves, and branches. This allows oxygen to somewhat be there, but also deprives the items of drying by sunshine/wind. Fungi will naturally accumulate where things are kept moist and dark. This will rot the woody material in time. Plant shrubs and trees around these nutrient sinks. I would just leave them there to act as nature would like, they are great habitat for birds and other beneficial creatures.
I have to disagree with Travis with burning being the best option for your woody debris. From what I have learned in my conversations with modern foresters around my area, is that the more debris that is left, scattered, in the forest, the better for the landscape. This will encourage fungal growth, and create a lot of micro habitats for myriad living beings. It will look ugly for a short time, but as the plants recover the landscape, you will notice that you will have gains in diversity where this debris is laying. You can lay this all strategically so that you can walk more freely in the meadow without worrying about tripping over anything. The swales can be your primary paths, for instance.
I would broadcast the grass/clover mix on the area, and lay out the logs and such, and worry about adding soils later, by wheelbarrow where you think you have the most stability.