Maya Modeling :: Cover Large Areas With Grass And Vegetables

I have a scene showing a wide plain heading towards low mountains. The perspective is such that the mountains appear to be about 1/2 a mile away, across a basic southwest desert plain covered by dry-looking yellow grass, sagebrush, some cactus, etc.

My problem is how best to cover the plain with grass so that it's covered well enough to look realistic. Paint Effects works beautifully, and eventually I'll place clumps and varieties throughout, but covering such a large area by painting short grass all over is time consuming. All I've seen by searching online suggests using Paint Effects to paint in grass, which works, but it's extremely time consuming. If the only way is to spray a little bit then convert it to polygons, watch the coverage drop due to the polygon count, then repeat the process...something tells me this can't be the most efficient way.

How to more quickly cover a large area with decent looking grass. I suspect a nice combination of the right surface texture underneath Paint Effects might do the trick,.