Read up on hugelkulture, there is a complete forum to peruse. In my current home, I have inches of topsoil and then total clay. I started with raised beds of about 10" prior to finding huglekulture which helped the drainage issues. Whenever it rains, even just a bit, my backyard is ankle deep in water. The raised beds helped to keep the plants from drowning but in dry times, I had to water like crazy. I changed over a few of my beds into a modified huglekulture type bed as an experiment to find out if I could not only keep them dry but, would they take care of watering themselves also. I have to tell you, huglekulture is definitely the way to go for me and I think it would work great in your area also.
In traditional huglekulture, you pile up lots of wood such as logs in a pile about 6 foot high, cover with a bit of soil or compost and plant. As the wood begins to rot, water is absorbed and you no longer have to water the beds. My very small yard would have only allowed me maybe 2 beds so I did a modified version. It probably is not as good as the traditional one but it works out great for what I need. My beds were already 10" deep soil filled beds lined with weedblock. I dug out the soil and cut away the weedblock. I then filled them heaping with all the wood chips I could get and then put most of the soil back on top. The plants are thriving and I no longer have to water (well this year has been wetter than normal at the beginning but in times like this I still had to water if no rain in 2 days, this year NOT).
Anyway, take a look at the hugelkulture forum, I really think this is what may work for your situation. Kim