Mr. Smarty Plants concurs your intent avoid using St. Augustine to fill the gaps between your limestone blocks. To me Silver Pony foot Dichondra argentea (Silver ponyfoot)is a good choice, but as you read in the links below, it can produce runners up to 4’ in a year. This may be more trimming than you want to do, but its better that mowing St. Augustine.
Another possibility is a ground cover called Horse Herb Calyptocarpus vialis (Straggler daisy). From the links below, you can see that it has its proponents and detractors. It is fast growing and is considered invasive by some.
A third possibility is a native perennial ground cover called Frog Fruit Phyla nodiflora (Texas frogfruit).
Any plant that is growing in the gaps is going to require some maintenance. You will have to choose the best looking, low maintenance plant you can find.