A cover crop you can plant now is daikon radishes, also sometimes called "tillage radish". I planted some last year at this time with good success. Mine were purchased from High Mowing:
https://www.highmowingseeds.com/organic-non-gmo-tillage-radish.html. It says to sew in the fall, but I found they grow fine this time of the year, too. You just might not get good roots before they bolt. An another advantage to the radish is that pests really don't seem to like eating them--neither slugs nor ducks nor
chickens ate any of them on my propety. I never tried growing them in that degree of shade, though (mine were getting 3-6 hours of sun). You might also be able to plant peas, too, as a cover crop. But, I don't know how "field peas" (usually used as a cover crop) would do, but I know snow and snap peas do well when planted now.
As for sewing the seeds, daikons--and buckwheet, but it's too early for buckwheet--will do great if you sprinkle them down and either rake them in or cover with more mulch. I once planted buckwheet by throwing down the seeds, mowing the lawn without the bag so the clippings fell over the seeds, and then sprinkling duck bedding over the area. They did great, and they were over a year old seeds at that time, too!
As for perennials growing in the shade, looking at your picture, you're shade doesn't look like "deep shade." On my property, in similar areas, I've seen salmonberries, blackberries, thimbleberries,
nettles, oregon grape, red huckleberries (these do great in the shade!) and salal. For an edible ground cover, you could try miner's lettuce, Siberian miner's lettuce (doesn't taste as good as the other miner's lettuce), alpine strawberries and violets. Now, off course, these will produce better in the brighter areas, and not much will grow right at the roots of those trees except maybe red huckleberry and sword fern (supposedly the tubers are edible...I haven't tried that yet). You might also be able to grow licorice fern there, too, but I usually see that growing on/under maples. Other edibles that are said to grow in the open shade are hostas, bunchberry, and--I think--serviceberry. Blackcap raspberries, aronia, currants and gooseberries might also do well--I've got stink currants growing in that type of shade (they taste like pine and aren't very yummy), and my aronia is growing in about that much shade, too, but it hasn't born berries yet.
As for what to plant when, I love Erica Strauss's monthly
gardening chore guide (
http://www.nwedible.com/topics/monthly-garden-chore-lists/). I also like Seattle Tilth's Maritime Northwest Garden Guide (
http://www.seattletilth.org/get-involved/gardenstore)