Hi Sebastian.
Good questions. I wonder if you have any species of maple around, or if it's too hot. In your position, I would look for a tree that acts like a Sugar Maple, carrying out a process called hydraulic lift, where it basically pumps water up from the water table for use by itself and the plants and other trees around it. I had thought that some type of fig, or something else with a really long taproot, was tapped for this purpose in a few of the regreening the desert projects.
I think perhaps looking into the pioneer species available locally would be a good idea. If you had pioneer plants, weeds, essentially, and pasture plants that live for an extended period without rain, it would be good to get them in the ground before the rains come. They will cover any minimally covered ground, providing shade, reducing evaporation, and increasing water infiltration and groundwater recharge when it does rain, basically refilling your spring's underground reservoir.
I would then look at what comes closest to treed savanah in your area, and what the makeup of the grasses are. I would look at this at very least like a transitional aid, an ecosystem of nursery plants to care for the soil, which will then support your new trees.
You might also consider looking into
Air well (condenser) construction. These structures literally condense moisture out of warm air, and can be as simple as a pile of rocks.
The same principle can be used with a deep layer of rock mulch laid with enough airflow to permit the same process, and it provides the same benefit as organic mulch, in that it shades the soil, and soil life, from the baking sun.
Pictures would be greatly appreciated. Otherwise, keep us posted, and good luck.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein