Please suggest some Livistona species that can handle full desert sun and our winter lows.

Then, if you’re able, suggest where I can buy them.  Lol

I think the majority of them, atleast Australian species can handle Phoenix sun. I believe Rod Anderson has a few species including Livistona Nitida in his yard. Most are hardy to teens except Victoriae, Carinensis, and possibly Saribus. I’m not sure on exact hardiness but Livistona Alfredii has similar blue/pale green leaf color to Victoriae  but is hardier. Seeds are currently available and I had some thing like 90% germination. They are definitely slow at first and do better with shade as seedlings 

I can recommend Livistona mariae as being hardy to both heat and cold. My Livistona alfredii seems hardy, but I am still trialing it. Livistona victoriae seems to be the least robust so far.

Hi 76˚, Lo 69˚ rain most of the day

Mariae should handle the SW desert sun OK, as it grows naturally in the hot ( not as extreme as those US parts, but not far off it  ) Aussie outback.. Victoriae grows in extremely harsh local monsoonal escarpments in the Northern Territory, loves heat, but natual enviroment has never seen freezing conditions. Alfredii is also a heat lover, the parts of the WA Pilbars it grows in has similar summer temps to the Phoenix region, although again they dont see freezing temps in their natural growing range.

When I lived in inland central Florida, we had temps in the 20s every winter. L. saribus was bulletproof and showed no problems whatever, despite coming from tropical SE Asia. L. chinensis also did well.  Aussie Livs that I had did very well, too.