Another view...

Dwarf hollies may be your best bet although Japanese Fringe Flower will usually bloom at least a couple of times a year and will tolerate some shade (at least mine did).

I have an area similar to yours and have planted camellias, hostas and ferns that do well.

my camellias grow slowly but are covered in buds. They only get dappled sunlight with maybe some brighter light occasionally. No, not even 1 hour. They would like more.
Isn't there a dwarf oakleaf hydrangea? They need little water.

My current passion for part sun are the dwarf abelias. Kaleidoscope is my favorite. For some plants, you might try ajuga and that purple jew which isn't a wandering jew but we all call it that.

someone gave me some purple perilla that is happy in shade and multiplies like crazy. I like that deep eggplant purple. Maybe you will too. I'll see if I can find the actual variety name.

Perilla frutescens var. purpurascens (Perilla

Agarita (berberis trifoliolata) is a native evergreen worth considering; Turk's cap (malvaviscus arboreus var. drummondii) and American beautyberry (callicarpa americana) are good if you'd like some deciduous variety. All should do very well in shade (and benefit wildlife) most anywhere in central Texas.

One of my favorite east Texas natives in shade is Virginia sweetspire (Itea virginica) for its flowers and very long enduring fall color on a surprisingly small amount of sunlight... at least in our DFW location. We have the 'Little Henry' compact cultivar (~2-3 ft). Seems to have a bit more tolerance for mildly alkaline soils than some sources claim as ours is doing well where the pH typically tests in the 7.0-7.2 range. Though probably not a good option where pH is much higher.

I still like leatherleaf mahonia (mahonia bealei) and any of the nandinas for this sort of shaded foundation location, but should consider the local invasiveness potential before planting any of the berried varieties - especially if you're within a bird's BM of substantial wild spaces.