Groundcover to replace grass--need suggestions, please
Hello--I am looking for suggestions for a groundcover to grow on a sunny SE street corner that slopes steeply. The soil is red clay and the location hot and fairly dry--but moist enough to keep the grass green. It is at my husband's business and is currently covered with a mix of bermuda and other weedy grasses. He wants to be able to stop mowing altogether because the slope is very steep and the ground very uneven, which makes mowing difficult and somewhat dangerous. Because it is a street corner, the plants have to be kept short so drivers can see. To make matters more complicated, there are all kinds of buried utilities there also, and the "boxes" and meters for them are there, too. (The utility companies like to dig around quite a bit, which is why the ground is so bumpy.) We can't plant anything that will hinder their access to their equipment. Also, we don't have much money to spend on this project.
OK--so this is what I want to do. Kill all the grass with a herbicide, leaving the dead turf on the ground to stop erosion and avoid digging. Plant one or more kinds of low-growing groundcovers that I can grow from seed, either by starting the plants in pots, or (even better) by scraping up lines in the dead sod and seeding the slope directly, as you might overseed a lawn. Does anyone know if this will work? Also, can you recommend any plants to try? Would creeping thyme work? I'm also amenable to planting native plants, even "weedy" plants, as long as they are low-growing.
I'm sorry my question is so long, thank you for reading it. I'm open to any suggestions!