Hi,
java moss on a grid should work just fine, but most types have an unruly growth pattern, that is very different from grass. If you use 'erect' moss or 'christmas' moss you´ll get a more evenly grass carpet. Alternatively you can cut open marimo-balls and put them onto a grid.
Eleocharis sp. is definitely looking most similar to grass, but requires more lighting than java moss.
There are dwarf forms from Sagittaria subulata in the aquarium trade, that grow quite well under low light.
Both plants are suitable for coldwater.
Best regards,
Jens