It would seam that you could grow greens in beds throughout the winter?
Rape is more tolerant of heat and warm soils than what you mentioned. Here, I can get more for the dollar growing it. I grow it to full height, and cut and carry. I do not know what it would cost for you to get the seed etc. It is a more economical "field crop", over a "garden vegetable".
I do like to grow turnips. Once I am out of pumpkins and winter squash, I turn to turnips. I impale them on a nail with the tops in the house. I replace them as necessary. It gives them something to peck at on the coldest days.
I noticed that your area was seeing more rain than what is typical. It made me long to visit. I love how it smells in the desert before and after a rain.
Right now I'm rather limited to garden beds because our soil here is practically sterile. We live on what used to be a quarry and I'm finally in a position to start working on soil improvement...with help from my chickens. The area around my house is open range and I actually collect some of the cow manure to add to the soil, along with decaying straw, leaves, pine shaving, and anything and everything I can turn into compost. Eventually I hope to grow various grasses, clover and other mixed cover crops for the chickens to forage as our "nut grass" is pretty awful....hardy, but awful.
My garden itself is pretty small and other than tomatoes and lettuce, which my family consumes in abundance, I've decided to devote most of the available soil to consumables for the chickens. As I'm able to expand the area I look forward to adding more variety. I've never attempted to grow rape. I'll do some research on it. Thanks!