Another thought I had: would using seed be practical? Probably cheaper but I don't know how long it takes or how hard they are to grow from seed.

If Sedum 'John Creech' is hardy in your zone (and pet safe--probably is), it's handsome and does well in both sun and considerable shade. Spreads fast too. Can take some foot traffic, but not constant.

How big an area are you talking about? And how deep? You can also look into large plants such as Blue rug juniper for sunny areas. I planted some a couple of years ago that are now about 3 ft x 3 ft.

Sedum will not hold up well to any foot traffic. It is too succulent and squashes/crushes easily. Ideally, you want a single type of ground cover, preferably evergreen, that will tolerate both sun and shade, which eliminates the thyme and phlox (full sun only). I'd look at something like Cotoneaster dammeri. There are several culitvars recommended by the Chicago Botanical Garden and the Morton Arboretum, like 'Lowfast' or 'Skogholm'.

Not very many groundcover type plants are available from seed although sometimes you can get growers plugs.

Sedums are fantastically quick and easy from seed though. I bought a mixed lot of seeds for 'green roof's and such - had around 14 species. They germinated quicksmart after late summer sowing, grew under glass all winter, and now fill several seed trays...for the lowly layout of around 7$. At that speed, ease and economy, what do you have to lose by sowing a few trays yourself (didn't need heat or lights).

I am watching a brutal contest between violets and lamium orvala at the moment - irresistible force meets immoveable object. I can attest to the resilience of these...and are amenable to a ferocious strimming if they need reminding of their manners.

Phlox holds up nicely in full sun circumstances where the soil drains adequately, which certainly depends on how close to or far from Lake Michigan you are. I use Phlox sparingly based on our soil types in the south burbs unless the beds are elevated and the medium is amended/improved.

Sedum 'John Creech', Sedum kamschaticum and Sedum kamschaticum var. Ellacombianum have long been "go to" selections for me. Sedums will not, as Gardengal mentioned, take much more than causal foot traffic. You would be better served putting stepping stones through the bed where you anticipate foot traffic.

Here are job pics of Sedum spurium 'John Creech' and S. k. 'Ellacombianum', both in the south Chicago burbs. Creech is the shorter and less aggressive of the two based on my experience. I also have both at my personal residence and they perform wonderfully. You can source any of the Sedum selections from Chalet in Wilmette or Gesthemane Garden Center in the city. They would routinely be in 24 count or 32 count flats, individually celled.