I have dwarf Monkey Grass growing in shaded areas where my St. Augustine refused to grow. Like you, we have some clay to deal with but mostly hard compact soil because of the trees' roots sucking up moisture. This doesn't seem to bother the Monkey Grass. It seems to grow in all places, albeit slowly except right up next to a tree root. I douse it 2 times a year with bags of Miracle Gro Garden Soil and it seems to love the boots. I mean boost. hahaha No it doesn't like constant boots on it. It seems to pout when I roll over it with a wheelbarrow getting to and from my projects. But it bounces back and forgives me. I don't think it would be bothered by a few kitties rolling on it?
I bought 1 gallon size and separated it. I planted them about 3" apart to let them grow together. It takes awhile. I would plant larger clumps closer together if I were to do it all over again.