Plant the hair grass deeper. Your substrate is a fired clay, correct? It is light weight and easy on delicate plant crowns so deeper is fine. My hairgrass will grow crowns 2" below the surface of the substrate at the tank pane! I take the tiny clump by the roots with my forceps [works better than tweezers for me] and pull the plant under the substrate so the crown is maybe 1/2" covered by substrate. Let go of the roots and pull the forceps out at an angle. The one time I did this with no water in the tank the plants stayed down better as the substrate falls around the roots when the tank is filled. When you plant in water the plant can float up as you remove the tool as you well know!
Lots of other grassy carpeting plants to choose from but any that form lots of tiny crowns and fine leaves are going to have fine roots too. Blyxa japonica sort of looks like a clumping grass but is really a stem plant with thin leaves. The stems easily break before roots have grown into the substrate so aren't very easy to deal with either.