Ask Mr. Smarty Plants

Have you considered Astroturf? But wait, that hasn't been designated a native species (yet).

Finding a pleasing ground cover under your conditions is challenging. I like your idea of sedges. Carex planostachys (Cedar sedge) is a common sedge growing wild under cedars in the Austin area, but it may be hard to find seeds or inexpensive plants. An apparently similar sedge is Lawn Sedge, Carex leavenwothii, available from Pat McNeal, a local grower. Sedges might have to be put in as plugs of the intact plant rather than seed.

A lot of people like the looks of Horse Herb, also known as Calyptocarpus vialis (Straggler daisy). It would nicely complement your sedges and is not so invasive that you couldn't get rid of it by acting promptly if it doesn't satisfy you. It is low-growing and therefore scoop-friendly.

If you do not want to fill in the boggy spots in your yard, consider Carex blanda (Eastern woodland sedge) or Carex texensis (Texas sedge), both of which prefer moist soil. These latter two grow somewhat taller then Lawn Sedge. Carex texensis is available from a California grower, Greenlee Nursery. Thelypteris kunthii (Wood fern) would look good if planted out of the direct path of your pooch. Chasmanthium latifolium (Inland sea oats) is also a good bet. During the summer it sends up flowering heads to about two feet, so it too should be placed out of the beaten path. But it is tough, and the seed heads are very attractive.

Click on the underlined plant names above for more information on each. I attach representative images below.