The dwarf monkey grass sounds like a good idea.
I did some research and hope none of these will be harmful for the cats. Some could be considered invasive or at least aggressive. A few of these may be too tall, or will be until the cats get comfortable rolling around and flatten them a bit.
I once saw a blog where the person was testing plants for a chicken coop and she planted each type of plant in a flat, moved the flats around to get the best location for each, removed the plants which did not work before planting in-ground.
Callirhoe involucrata/Purple Poppy Mallow
Dichondra carolinensis/Pony Foot
(No photo in our database but there is another called Silver Pony Foot)
Glandularia bipinnatifida/Showy Verbena
Hydrocotyle umbellata/Manyflower Marsh Pennywort (It's good old Dollar Weed )
Oeonothera speciosa/Pink Evening Primrose
Oenothera macrocarpa ssp. macrocarpa/Big Fruit Evening Primrose
Phlox divaricata/Wild Blue Phlox
Phlox drummondii/Annual Phlox
Phlox pilosa/Downy Phlox
Phyla nodiflora/Frog Fruit aka Turkey Tangle Frog Fruit
Salvia roemeriana
