I have little experience with your heat, but these will take our heat and humidity and are more than hardy enough for you and IME work as spillers for pots. One of the classics is gold creeping Jenny, Lysimachia nummularia 'Aurea'. Just don't let it escape from the pot and root in your garden or lawn since it can be a total weed there. Periwinkle, Vinca major and V. minor, both have variegated forms that are classics for containers but you want to avoid letting it root in the garden since it spreads also, though not as vigorously as the all green variety. I've used some of the creeping thymes and prostrate rosemary in containers. There are now some named Heuchera and Heucherella varieties such as the Heucherella Falls⢠Series that are trailing and would work as spillers, but I think might want some shade in Houston.

Also, if this interests you there are quite a range of perennials that are only hardy in higher zones than yours, but if you have a spot like a garage with a bright window to move it into for cold stretches, they could be wintered over and work well for you. For instance Dichondra argentea 'Silver Falls' is only hardy to zone 10, but is perennial in places without frost.

There are lots of hardy herbs that are commonly used as ground covers that also make great perennial spillers in containers. Corsican mint is one. Creeping thyme is another.

Many alpine or similar varieties of strawberries are also beautiful spillers, in leaves of course but also with dangling berries. Many are evergreen in your climate, and heat tolerant.

Ground morning glory, or Convolvulus mauritanicus is another idea. The blooms are beautiful!

Here is a link that might be useful: Corsican Mint

One that used to be used a lot in hanging baskets and containers around here but hardly seen anymore is trailing nepeta, it comes in both plain and variegated foliage.

Another that goes dormant in winter but comes back in the spring is Kenilworth ivy (Cymbalaria muralis ), a pretty little thing but you have to keep an eye on it it has the habit of spreading itself around.

Actually they have been selling Dichondria argentea in Texas for eons amongst the native loving crowd. It is a standard in Nurseries here that have a stock of natives. It is native to the Big Bend area of Texas and Tucson . Big bend area is Z8b - 8a. Tucson is Z9. I have been growing it for 30 years in and around Austin and it was only damaged when we had a freeze to 12F. It comes back up from the roots every year. I think it grows in moist canyons there because it appreciates a tad more moisture than desert xerics. The common name for it in Texas is Silver Ponysfoot. It is a great spillar for pots and raised beds and will appreciate a draining soil in houston. It wanders all over my garden. I love planting tires with it.