That light sounds like it is about right for the tank, mine has water 22cm deep and I have that TYPE (LED) of lamp 6W, 6500K, 500 lumens. I tried some grass that I bought that was on a metal mesh that had a plastic coating over the mesh. It didn't do very well and went a bit yellow (didn't die though) so I don't know how well it would grow, but would give it a go anyway, there's little to lose? I removed it as the plastic started coming off the mesh and the mesh started to rust - looked horrible? All plants take some time to settle in though so may look a bit uninspiring for a while until the roots establish? In my newest tank ALL the plants looked bad for a while but none actually died and now they are flourishing (too bloody well)!
I found this link which may help you decide? I assume you are using a soil substrate?
https://www.aquascapeaddiction.com/articles/dwarf-hairgrass-carpets-made-easy
Your actual question though I can't help much with and will hope others will help there. My philosophy is 'try it and it either will, or won't work', but the grass I tried was the only plant that I have ever discarded and that wasn't really anything to do with the plant, more the mesh it was supplied with?
The only other thing I can think off that is related is, lots of people use CO2 with grasses etc, but this is best avoided and not necessary as it will live without it (It would do better with CO2 but the risk to shrimps is too great to warrant it, only use CO2 for a plant only aquascape tank).
Simon