Sun is really at a premium here, as is often the case in your area. I would take out the smaller trees and vegetation to the left of the garden site and intentionally replant it with a lower story of fruit/nut trees. There are many, many plants that will grown in dappled sun, part day shade. Additionally you can plant things that will grow up the trees -- curcubits are particularly good at this and might even like the back with the diseased arbovitae. Once you get a food forest there, you could work back to the area with the deep shade (conifers) where you could grow a NW forest area with huckleberries, mushrooms, etc. As for cover crops, my fav is always peas. Tons of green manure and great eating. they go in as soon as the ground thaws and will be done in time to plant a warm weather crop. You an cut down the vines to use as mulch or mow them down, dry a few days and work them in.
I'm trying to rehab an area in the flood plain and while I do want conifers down there, I also know that they can only be there b/c the water table is high. They are not very deep rooted compared to their stature and therefore have many many feeder roots sucking nutrients closer to the surface. Take a few hikes. You will see that the area around these trees needs to be covered with shrubs that make leaves and do not have competing root systems: dogwood, rhodies, azelea, huckle-salmon-gooseberries and currents on the sunny side of the tree. I've lived with these guys -- first in the redwood forest and then in a yard with two full grown fir trees-- it's hard working with them in a small space, too expensive to remove them.
Also, native plants may be available from your area conservation district.