Basically, it's a waste of time. You won't get enough nitrogen to be worth the energy it takes to collect the seeds and scarify them for sprouting. If you just scatter them they won't sprout for years. What your vegetables need is planting on the Phoenix AZ planting calendar - not the seed company's - drip irrigation, and thick mulch (6 inches of shredded palo verde and mesquite branches) to help retain soil moisture. I took my dirt patch from digging holes with a pickaxe to being able to dig anywhere in the bed with a trowel with just thick mulch, semi-finished compost, and drip irrigation. If you want to improve the soil, plant okra. It loves the heat, has deep spreading roots, and it's edible. After the plants stop producing, cut them off at ground level and leave the roots to rot. You can even use okra to shade other vegetables, such as chilis, that prefer afternoon shade. Plant the okra along the south and west of the bed and the less sun loving plants on the NW side of the okra. Try the AZ forum for help with our specific arid alkaline dirt problems and hot growing conditions. Here is a link that might be useful: Maricopa County veggie guide

Desert trees won't survive in a lawn. They'd grow tall and fast and either die of rot or be constantly broken by the wind in their low dense pithy wood (from overwatering). You want xeriscape do it all at once. Piecemeal won't work. Now you could plant desert trees and totally cease watering the lawn as a non-HOA approved compromise. The eventual and I do mean eventual (slow growing desert trees) shade would further kill off any surviving non-native grass.

Local plant propagators have made giant strides over the last 40 years to introduce a wide variety of species that can handle our salty soils, challenging climate, indigenous pests and diseases, as well as brutal maintenance practices by some landscapers. Mountain States Wholesale Nursery in Litchfield Park is one. Just take a look at their web site and you'll find trees (65), shrubs (120), groundcovers (21), grasses (22), vines (6), succulents and accents (74), perennials (48), cactus. New introductions are being tested all the time. Other growers include Arid Zone Trees, Arizona Wholesale Growers, Desert Tree Farm, etc. The University of Arizona does research on salinity tolerance, diseases, cold resistance, water demands, etc., but leaves the introduction of new species up to the commercial growers. Here's a link to a database with over 600 desert-adapted plants including 128 trees. Some that might interest you include Silk Floss, Jujube, Carob, or Chinese Pistache. BTW, oranges are easy to grow here but as land became more and more valuable, taxes increased and the costs to pump or buy water to irrigate orchards became prohibitive, owners sold their land. Here is a link that might be useful: Water Wise Plant Database

I just lost the very same tree. I live in Arizona and ours didn't bloom this year so we checked it out. Same issues as yours, we lost all the leaves and the ends of branches were turning brown. Then we noticed that the usually green trunks were turning gray. It was a boring type bug. It is coming down now off it's own, because it looks to be dead. We did ask around to experts, there is no help for it. So sorry. I was so sad to lose my tree, it's so pretty in spring with all the flowers. Ours was well over 12 years old. I wish I could give you some advice to save it, but we were told there is nothing to help.