I have not heard of Mejia grass, might you mean bahiagrass? I've no experience with it, not being from that area, but this Clemson article might be of interest:
http://www.clemson.edu/extensi...
You could also ask your local extension office what they suggest.
Doing a whole acre all at once is certainly quite a task. Can you not, as Greene suggested, do it gradually? One can get large areas of plastic although you'd also have to have a method of keeping it anchored.
If using a herbicide, any residual effects and soil activity would depend on the specific herbicide used.
I'm assuming Rusk County would be your nearest Extension office, in which case contact info is given here:
http://rusk.agrilife.org/ag-na...
