If you are looking for a way to both conserve water but also have a healthy garden, an Olla might help.
While surface watering, some of the water will be lost to evaporation, and you may not get the soil damp enough to encourage the roots to spread deeper.
This is when the Olla becomes helpful; made from porous clay, this pottery can be filled with water, which it will then gradually seep into the surrounding soil. While most of it is burred, enough of the neck is out of the soil to fill it.
You can make your own for your outdoor garden using terracotta pots and water-proof adhesive. Simply glue two pots together, and fill the hole on one side. When the glue is set, just bury the pots (with the unfilled hole up), fill with water, and cover the hole with a saucer, cork, or rock.
If, however, you only have indoor plants, you have an option, too! You can get terracotta watering spikes that work in a similar way, but a glass bottle fills it.
While they might not be suitable for all plants, for many plants they are suitable, and can help with your gardening chores.
While they might not be suitable for all plants(such as plants that prefer dry soil), for many, they are.
Images from Permaculture Research Institute
These do originate from very hot and dry climates, so I agree there might be a leak in yours, or perhaps you are trying to water too large of an area with too few of Olla's.
I am in Alberta(Canada), and it did work here during our droughts when we were also dry and hot last summer, with temperatures comparable to Texas (at least according to your averages online).
However, drip lines are a good choice, too! I quite like them paired with rain barrels and battery-operated faucet timers(for automatic watering). Though I don't know if rain barrels are legal where you are? I have heard they are illegal in some places in the USA.