Columbines are my favorite easy growers. Although there area few places in my garden where I deliberately sow some named varities, I mostly just strip the seed pods off in August and scatter the seed by hand in areas that I want to see them come up next Spring. It is always a delight to see what new ones come up. The original clumps from which I get these seeds are now badly overgrown, almost as if the Columbines were a weed, but since these areas are out of normal sight, who cares! The seed comes up in Sun Or Shade and I don't make any attempt to formally hybridize Columbines, just enjoy the new ones.
I have not tried sowing Columbines, just ordered some plants and tried them in about a half-dozen places. All of them did okay the first year, but none of them have come back. Some started to come back, but didn't seem to last long and never flowered. Others didn't return at all.
I had noted them as something to give up on, but "easy growers" caught my eye, so maybe I'm doing something wrong? We have a lot of trees, so most were in mostly shade, but a few were in morning shade and afternoon sun. Like I said, they all bloomed the first year.
I'm pretty sure they don't like "wet feet" especially over winter when they're dormant, but I don't really have a clue about AZ conditions. Maybe you could ask at one of your local nurseries (you know, one where people actually know about plants!) and see what they know about growing them in your area. Sorry to not be of more help!