Tilling will only exacerbate the problem, and deposit fresh organic material down into the soil, where it still can't be "used" by roots until decomposed. Nature's plan is for decomposition to happen on the surface.

http://permaculturenews.org/2013/09/20/soil-not-dirt-dr-elaine-ingham-talks-soil-microbiology/

Plenty of plants are suited for the conditions you describe, but it sounds like you're having a "dirt problem," not a sun/heat problem, to me.

First, I agree with Tiffany. Going on - You did not say when you planted the garden. A good time to plant shrubs and perennials would be mid to late October; they will have enough time to establish themselves and get good root growth before winter dormancy sets in, but because of cooler temperatures will have a lot less water demand. The mulch was a good idea, though I might have used straw instead - less acidity, plus as it decayed it would add organic material to the soil, and most Alabama soils can use more organic material! Admittedly, not as attractive as cypress.