Answer: Strawberries really require more sunshine than you can provide. While the plants will grow in the area you describe, they won't flower or fruit as well as plants in full sunlight. Wish I could be more encouraging!
How about a different kind of ground cover type plant in that area? Your choices include Corydalis (with a profusion of yellow flowers), or Fragaria chiloensis, a wild strawberry, with edible berries (small and pulpy as opposed to regular strawberries. Both plants will grow well in semi-shade.
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