I've tried a few different varieties, but none have survived. Don't bother trying Stello D'oro- I've tried twice with no luck. I've heard the evergreen varieties are best for hot climates like ours.
They might be called "full sun, drought tolerant", but that's in Pennsymvania and England.
In AZ, give them morning sun, afternoon shade and regular deep watering. Pamper them for the first summer until they get a good root system.
I've tried a few several times over the years and they've all failed eventually. I know a lot of other gardeners who have had similar results too, LOL. They just don't do well here.
That being said, the beautiful Royal Palms resort in Phoenix has a few that bloom off and on all summer. They're in dappled light and look pretty good (they are the evergreen type as you suggested since evergreen types tend to not need/want as much winter chill as the deciduous types). Even so, they don't look as lusty as they do in the midwest etc.
Take care and happy gardening,
I have a huge bed of daylillies in my yard. I ordered several assortment of varieties from a couple different mail order nurseries a couple years back and planted them all in a row. They're literally in the middle of my yard, so full Phoenix sun. They get watered with the grass daily, and they have done great. This year, several of them produced babies along the flower stems, so I'll be potting those up once I get a chance.
The mail order nurseries that I ordered sent different qualities of daylillies too. Some were obviously older and some were less than the highest quality. But, all survived, with little to no babying. They bloom for me all spring and fall.