You could try something that doesn't need nitrogen fixation, something that is well adapted to the soil and climate of Albuquerque, like
Indian ricegrass. It is possible to buy the seed in New Mexico, so you wouldn't have to go collect it. With a little help (plant it, help it germinate with a little water, give it a little compost at crucial stages), you could raise a good stand of it as the first crop in your succession. Or, since it is a perennial, use it as a backdrop to your whole permaculture.
There aren't a whole lot of possibilities given your climate. Rather than try a cover crop mix adapted to wetter climates, go with what is adapted locally.