If you are dealing mostly with sandy/rocky soil you've got drainage in abundance. It's possible you have a perched water table with the caliche - but if it's 2 feet of permeable substrate in a desert environment I don't think you are going to be dealing with enough water for it to matter, you'll just get lateral drainage. What you need a way to slow down infiltration, and also stop leaching since the cation exchange capacity of sand is hot garbage. Shade + organic matter is probably going to be your go-to tools. Unfortunately I don't think the free arborist chips solution I did will work for you - might be too arid for them to break down in a reasonable time frame. So it's either import it at cost, or plant and wait. Just boils down to your level of patience vs stomach for paying for "dirt" as it turns out good soil isn't actually "dirt cheap".

Something to consider - most of the no-till / permaculture folks admit that a one time tillage up front isn't that bad. The main issue with tillage is you are disrupting an ecosystem. The fungal networks, the worms, all the little critter infiltration tunnels. But that only matters when you aren't dealing with dead compact degraded soil. Right now there is nothing to disrupt, so if you can combine a one time deep tillage of organic matter, or maybe subsoiling to break up some of the caliche to whatever depth you want - now is the time to do it.