For that exposure, why not try a clematis? They can put up a nice viney foliage screen and will bloom. The type 3 is easy maintenance as it blooms on new growth (you can cut back to the first couple sets of buds in late winter - I'll be cutting mine back probably next weekend). They have a main bloom in early summer and a rebloom later in the season.

Hi and welcome to Houston!
Creeping fig - evergreen, no flowers (though there's a varigated type.) They get pretty rampant. you'll see them a lot in Houston on the walls. Very easy care. easy to find in landscape places, they're often already kind of large.

Grape ivy - sold as a houseplant sometimes.

I'll think a little harder to see if there are more flowery options. I'm imagining strong afternoon sun? trumpet creeper's fairly rampant and would probably work. a lot of people hate this plant for this. But it's pretty and you'd have better control over it in a container three floors up.

One thing - no matter what, you/DH will have to water it a lot. that's pretty much a given for TX containers.

clematis dont do well in Houston,its too hot here

bonnie - if the OP's balcony is facing N-NW, then it won't be getting blazing hot sun. As long as it is watered well and back from the rail, it may do okay. As it is, they are often grown in hot mediterranean areas - particularly the group 1s that maintain a permanent vine structure.

I went walkabout for a while...thank you for your suggestions! Am just now getting back to this part of the project. I have seen creeping fig everywhere, and it looks great...a nice cooling mat for the wall, and small enough in scale for the tiny balcony... We have yet to determine just how hot the balcony will get...we are on the 12th floor, and I don't know whether that means more or less mitigating breeze. We get lots of morning and afternoon light, but not much direct sun.
Thanks again!