For groundcover around blueberries, strawberries (both wild and domestic) are a great choice. You could also do creeping raspberry (has little orange rasberries) or lingonberry. In shadier areas, you could do bunchberry. Pansies are also a great choice, like Jordan said. The slugs are all of mine, though. You could also do sheep sorrel--it doesn't seem to mind it wet. It does spread, but it has a lovely lemony flavor. I also like
dandelions under my blueberries, as the flowers bring pollinators. You could also probably grow chives &/or green onions with the strawberries. Those all seem to do well with my wet, pacific northwest soil (though mines gravelly loam, not clay--you probably live south of Olympia, right?) All those plants could also grow under your trees.
Jordan has a lot of fantastic suggestions, for the non-blueberry areas, too, and I ditto all of them. The radishes will get tall unless you chop/harvest them before they bolt. BUT, at least in my soil, they self
seed, and so I never have to plant radishes--they plant themselves! Nasturtiums are beautiful, and also often self-seed, and can handle a lot of weird soil and weather. Another edible ground cover that self-seeds is Salad Burnet. The young leaves taste a bit like cucumber. Oh! And parsley is great, too. I planted mine once, and it's self-seeded for years and I've never had to plant it again. You could also plant daylillies--not really a ground cover, but they'll do well there and are pretty.
I also don't think you'll need the groundcloth under the blueberries. Mine do fine with just a
watering every few weeks, unless it's really hot. That was when they were young, too. I probably don't need to
water at all, now. Also, adding a thick layer of tree timmings/mulch/bark/woodchips under your blueberries will be great for the blueberries, hold in all that winter/spring rain, and keep down weeds. It also looks nice. AND, the strawberries will grow merrily in there, too.