I don't know if this method would work for your situation, but I thought I would pass it on. I heard of people cutting out the center of grass clumps with a reciprocating saw to remove the die-out that occurs in the center of the clump. Then they fill in the center void with soil to regenerate growth in that area. Seems to me, in theory at least, that you could use a reciprocating saw to remove the perimeter of your clump to reduce it's size. This would be a whole lot less work then digging up the entire plant and dividing it.

Here is a link that might be useful: Dividing grasses