Hi SBG,
If you're worried that about the depth of soil, you could always make a few raised beds to allow for more depth for say root veg.
In my top garden it too only gets the morning sun. In high summer it is shaded by about 1-2pm.
In my beds I grew...
Earlies - Swift
Sweet Corn...Once the potatoes had finished
Radish
Mixed Leaf Lettuce
Beets
Onions
Using the square foot gardening method.
As you can see (my lgreenhouse is 6x4, my little raised beds aren't that big, but I grow everything very close together.