Hello and welcome!
I don't know of anyone breeding Sussex in the area, but I can give you plenty of input regarding good birds to have for this hot desert environment. I will, of course, celebrate the Naked Neck Turkens (and NN hybrids) as most here know it's my primary breed. I honestly believe they handle heat better than any other bird out there, and my top layer produced 250 eggs per year on average for her first two years and so far in her third year has already laid over 200....all X-lg in size.
Additional breeds that do really well out here are Australorps (
@BlueBaby breeds gorgeous, healthy ones), Barred Rocks and White Rocks, and Rhode Island Reds. Easter Eggers and Silkies also do well, and many other breeds that might usually struggle in the heat do better here when raised for several generations by local breeders. And, of course, Leghorns and Fayoumis do very well out here, but they are flightier birds than many of us prefer.
I've also been pleasantly surprised by Silver Grey Dorkings, which I took on a year ago as my endangered heritage breed to work with. They've proven much hardier in the heat than I dared hope they'd be and my girls laid very well during the worst of the heat with minimal cooling assistance...just shade, plenty of drinking water, and a small stream of flowing water to stand in or scratch through.