Hmmm, ideally the grass would be done on cards of some sort depending on the level of detail / distance.
Perhaps converting to nurbs does this ???

But basically if the grass if far far away you could deal with large chunks textured onto polygons, and as they get closer to camera the chunks get smaller and smaller to get the paralax / depth you need.

The grass being drawn infront of your converted bushes is due to the grass being rendered as a post process as it is un un-converted paint effect.

Maya renders your scene without the grass then calculates the grass and just pops it on top. This isnt best practice and should be avoided, however you could just render the grass seperately and layer the other elements in afterwards. This would only really look good if you could get a z depth channel out for the grass which im not sure is possible with post rendered paint effects elements.