Another possible consideration could be one of the microswords - Lilaeopsis spp.
There are several different species of them -
L.novaezealandiae, so far as I know, is naturally the shortest of them.
L.mauritiana &
L.braziliensis are both a good bit taller but look extremely grass-like. Their downside is slow growth & thus it either takes ages to grow a carpet of any size or else you spend a fortune on starting it because you have to buy a ton of plants.
Another option would be one of the Helanthiums.
H.tenellum Green only gets to about 3” tall and bears a resemblance to baby spider plants that are all green.
H.tenellum itself might work but gets taller - six inches or so. Sometimes labelled
Echinodorus tenellum or
E.latifolius. Used to be called Dwarf swordplant.
H.bolivianum or
H.bolivianum Quadricostatus are in between heightwise. Wider leaf blades look remarkably like spider plant without the stripes.
All the Helanthiums spread by way of runners which produce new plantlets at regular intervals and are slow to moderately fast growers in terms of speed. You can direct the growing tip of the runner as desired & once plantlets have rooted firmly and are a reasonable size they can be severed from the runner & will produce their own, helping speed up the filling in.
Vallisnerias and Sagittaria spread in this way too. The most commonly seen Sagittaria is usually called ‘
dwarf sag’ but it isn’t a dwarf plant. Depending on growing conditions it is capable of growing to over a foot in height though it doesn’t necessarily do so.
If you like it, there is nothing wrong with it but if you want something shorter that can’t grow taller, consider a Helanthium or Lilaeopsis.