There is clumping Liriope (L. muscari) and there is spreading Liriope (L. spicata), and one cultivar of L. muscari ('Big Blue') is grown from seed, so it swing both ways. I bought a flat of the L. spicata about a dozen years ago because I didn't know any better, and I'm STILL trying to get rid of the stuff: it went everywhere!
Lots of grasses will do just fine in the climate you have, Ken, but you're right that the clay soil can be a challenge, because it doesn't drain well (roots can rot easily). That's one main reason why herbaceous ornamentals struggle in the South (aside from the heat).
What I would suggest that you consider is the option of tilling in some good organic matter (or sand in the T. O. pen) into the top 8"-12" inches of that clay soil in area where you want the grass to grow. That will help it drain better. If the area is (even slightly) sloped that can help, too. You ought to be able to rent a small tiller locally: rear-tined models are easier to use.
Little Bluestem (Schizachyrium) is a native prairie grass, and I know of one cultivar available called 'The Blues' that gets to be about 2' tall: there are online sources for bags of seed for this, too.
The Festucas are the blue fescues that you probably have in mind: there are several cultivars, most of which grow to 12" or less.
Carex flaccasperma is a nice blue native grass, too, and Panicum cultivars are worth a look but they get quite tall (3' is on the short side for these), although that could be kindof cool if you have the room. Sorghastrum is a native prairie grass that tolerates moist soil but gets to be 6' tall, which might not be practical for you. The turtles would probably love it though!
That should get you started. 