Ask Mr. Smarty Plants

I called Native American Seed and asked about growing the shade - friendly grass mix in your area.  They said it would grow there and would make a good meadow but might not be suitable for use as a turf grass.  It needs at least two flushes of growth a year.  So you could mow it at the end of spring and again at the end of summer.  Also, if your area gets too much rain and the soil stays too moist, some of the grasses will overgrow others.  This will be especially true of Inland Sea Oats.  But if you plan to have a little prairie instead of a lawn, this mix would work well with some prairie flowers. You may have to grow something else directly under your trees, in the deepest shade or just mulch there. 

They also suggested that you use Texas bluegrass for a lawn grass because it takes cutting but stays short and may not need much mowing.  Here is a description of Poa arachnifera (Texas bluegrass) from the Native Plant Database. However, a mix of grasses is usually more successful because different ones will colonize different micro-climates within your yard.  

Another choice for you might be the Southeast Native Grass Mix from Hancock Native Seed Company.  This grass is described as good all the way from North Carolina to Florida to east Texas. You could also talk to them about using it as a lawn grass, if that is your intention.  This can also be mixed with wildflowers. 

Grass seed should be planted in the spring according to the tips for growing grass from  American Native Seeds. But you need to spend time getting rid of weeds that came with the fill dirt, getting a soil test, and either planting a cover crop such as cereal rye or just mulching heavily and then tilling the mulch in before planting in the spring.  You can find the directions for preparing a soil sample for testing and the form you need to fill out to send it in.  You can use a quart sized plastic bag and put 2-3 cups of your prepared dry sample in it, then put that in a small box.   

And from personal knowledge, I suggest that you be sure to kill/remove every plant from your area, especially Burmuda grass which may be a contaminant in the soil brought in by your builder or be coming into your yard from your neighbors.  In sun, it will outgrow almost anything .For more information consult the following:

Easy Lawns: Low Maintenance Native Grasses for Gardeners Everywhere by several authors.