I really like your design - it looks like it will take full advantage of your limited space by going vertical.
I just wanted to share my experience with "no-till" gardening. My space is limited and currently I only have 3 4'x4' raised beds planted with vegetables. When I built the beds, I covered the grass with sheets of cardboard, then put in layers of composted leaves and salt marsh hay. Finally, I topped it off with purchased garden soil (this was before my own compost pile got going). This was about 8 years ago, and I've never tilled the soil in the beds since then. When the plants have died back in the fall, I cut then down at the base, but leave the roots to decompose over the winter. I've planted a cover crop of crimson clover each fall for the past 3 years. In the spring, I top off the beds with a new layer of compost from my compost pile. I don't use any commercial fertilizer, and I've gotten good yields from my little vegetable patch. I'm a believer in the "no-till" approach, and I hope it works for you, too.
Good luck with your design.