I'd get the soil test but I gonna go out on a limb and predict the % of organic matter is going to come back very low. You'll want to see %'s in the 4%-6% range and that's not easily done in a short period of time. Aerate and top dress is a great plan but you'll also need to mulch clippings back into the soil, leaves too. Fertilize with a product that will stimulate the microbes in the soil. Restore is a good product but there are others out there. Look for something that has a grain meal as part of the ingredient list. Soymeal, cornmeal, or even Alfalfameal. But be fully aware that it will take time. You can go the Scotts route and you'll get much faster results but the chemicals do nothing to address the fact that you have crappy soil. Chems don't build soil fertility so if you make that choice understand that you'll be using chemicals to fertilize and deal with weeds and pest/disease issues for as long as you own the property.

I cannot be sure where you are, in the United States in zone 4 says nothing because that covers a wide range of soils and growing conditions. However, if your soil is clay, clay soils do not have a high clay content they are clay, then what it needs is lots of organic matter. Sand will do nothing for you and as previously noted you need to add 45 to 75 percent sand to clay to make enough difference to matter, and that sand will not help with soil nutrients like organic matter will. These simple soil tests may help, 1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top. 2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains� too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up. 3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart. 4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell. 5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

Not a bad idea. I have, many times, used the "flip method" of building raised beds. I remove the sod and flip the pieces over then pile soil and compost on top. The issue that I can see with your plan is this. When you place a ring of soil around the root system of a new plant, water becomes a factor. Especially on a slope. Plant roots will come to the surface to find water. If there is not deep saturation of the roots, then they will grow upward to find it. That happens easily in our clay soil because the water sheets right off the slope. We never want to encourage roots to surface when the plant is young and fragile. When it rains, they will no longer be bricks, but a mound of clay, soil and decomposing grass. Those young roots may actually head upward into your walls looking for water. They also will not serve as a weed barrier for long. The seeds of dandilions etc. that float around this time of year will LOVE the brand new open soil that is exposed. Crabgrass is a pain in the grass. It spreads easily by seed. Because of it's existance in your sod, I would not compost those pieces. The good news is, you have them flipped upside down and they have been baked in the sun. More than likely, you have killed the grasses and smothered the seeds. Leave your walls in place and in a few weeks take a flat edged shovel and chop them up then rake, mulch or plant grass seed on top. Keep your new shrubs and trees well watered and be sure of full saturation with each watering. Less frequent deep waterings are much better than 10 minutes a day with a spray nozzle on your hose. Use your walls for that purpose. Place a garden hose inside of your walls and allow a trickle to fully saturate the root balls. If you can't get a hose there, use a bucket and slowly pour the water. Don't pour it so fast that it sheets off the surface. Take your time. Know the water requirements of the plants you have in place. Water accordingly and your walls will be of help to you. But I would chop them up after their purpose is served and mulch or seed. That is just what I would do. Others may have a better suggestion from their experience. Good luck, and for future reference, covering the sod with black plastic for a few weeks prior to removal will kill many of the seeds and grasses that you don't want to spread to other areas when you relocate it.

I would suggest a raised bed stepping down hill. My garden has 2x6s on lower side and 2x4s mostly buried on up hill side.