Contact the Department of Neighborhoods P-Patch program and talk to them about how to make your most excellent idea happen:
http://www.seattle.gov/Neighborhoods/ppatch/contact.htm
Know going in that it will likely not be some quick and easy process.
If it were me, and I wanted to have someone able to vegetable garden in a planting strip THIS spring/summer, I would just put the word out here on the WSB and work directly with the most qualified and non-flakey person who responds and has a yearning to do it.
A note of caution, don't allow tilling of the soil to any depth without calling 811 and having a utility locating service come out and mark water and gas lines that are below the surface.