Ask Mr. Smarty Plants

Well, you could give it to Mr Smarty Plants!  [The Wildflower Center/U.T. Austin happily accepts gifts]

OK,  Expecting that this is actually a serious question makes it quite a bit more difficult.  As a general rule, we follow the Wildflower Centers Mission to increase the sustainable use and conservation of native wildflowers, plants and landscapes.  Kleingrass originates in Africa so it’s clearly not native, but since you’re trying to remove it, I’d really like to help.

The natural methods that Mr Smarty Plants normally recommends are well stated in this previous  Mr. Smarty Plants question/answer along with fair bit of other good advice:   Eliminating non-native invasive bermuda grass in Morgan's Point TX 

Examining these methods, they don’t look very attractive.

1)  “Dig up all the plants along with all their roots, rhizomes, and stolons”.  This should work, but involves probably a lot more work with a plow than would be preferable!

2)  Solarization is our favorite method, but then it is pretty hard to apply to 10 acres!

3) Judicious use of herbicides.   As proponents of natural methods, this is our last resort. This paper from the University of Arizona reveals that Kleingrass is relatively resistant to herbicides, but does list a few effective applications.

 Expecting that our natural methods are a bit weak-kneed for use on acres, you may do well by also checking with the Texas A&M Soil & Crop Program [Turf Answers 4 You], and  the Austin Extension Office.  As an example, this question to the Cooperative Extension recommends a varient on all of these as the most efficient route.