You can avoid the problem by doing the trick from THZ2. You'll need a texture with the grass, a texture without the grass, and a floor texture of the rock tiles. What you do is you make a 1 fracunit wide sector on the edge of the platform. What that sector is for is for splitting up the textures, by having there be two linedefs. One can have the upper texture, and one can have the bottom one. The downside, of course, is that you can actually stand on the edge of that sector.
You can see this trick done in Techno Hill 2 to make the conveyor belt texture not double up, instead having part conveyor belt texture and part metal wall. You can notice it being done by getting the Liquid Shield and hugging the edge of the conveyor when jumping into the slime. You won't sink all the way in, because you'll land on the 1 fracunit sector to split the texture up.
Admitably, it's not very elegant, but it is a workaround that does work without killing the framerate as badly as using an FOF on the entire stage.