I would try xeriscaping the area with plants such as Black Dalea, Prairie Acacia and Arkansas Yucca. These are all native to the Dallas area and should stay within the bounds of the strip.

Ty

Rosemary will grow there too, but it may get too wide.

you can put up a simple trellis on the side of the garage and plant some native honeysuckles(lonicera), or most any other vines.

i've had my native lonicera for 2-3 years, they are slow growers. i have a japonica (Japanese or Hall's honeysuckle), they are considered invasive and grow super fast and cover up everything, and the vines on the ground will root and become a ground cover. i also have a carolina jasmine, it grows fairly vigorously, but not as much as the japonica.

Texas Tea Bush (melochia tomentosa), santolina, artemisia, flame acanthus, bulbine, mexican hat (ratibida) are some of the plants that have done well for me in the conditions you speak of, although the flame acanthus will need hard pruning a couple of times a year to keep in that space.
Molly

Where can you buy melochia tomentosa? I did a search and only came up with one website, Native Enhancements. Has anyone purchased from them?

Is that Texas Tea Bush hardy in North Texas?

Marti, I purchased my tea bush at a local nursery (in the natives section) and I have seen it in a couple of other nurseries since then.
Lucas, this is the hardiness info on melochia tomentosa from the dave's gardenweb site:
Hardiness:
USDA Zone 8a: to -12.2 �C (10 �F)
USDA Zone 8b: to -9.4 �C (15 �F)
USDA Zone 9a: to -6.6 �C (20 �F)
USDA Zone 9b: to -3.8 �C (25 �F)
USDA Zone 10a: to -1.1 �C (30 �F)
USDA Zone 10b: to 1.7 �C (35 �F)
USDA Zone 11: above 4.5 �C (40 �F)

Molly

I have a similar area that gets baked near a sidewalk. I have blackfoot daisy, zexmenia, red yucca, four nerve daisy, salvia greggii planted there, and all do very well. You also might try guara, but it likes a bit more water, in my experience. Lamb's ears might work, too.

My folks had an old-fashioned rose of sharon and old-style nandina on the west side of their house in Dallas. They may have been planted in a 3 foot strip rather than a 2 foot one, though. The althea/rose of sharon lasted more than 30 years; the nandina is still there. They never pruned either much if at all. Their house was on blackland clay.