Go hairgrass! The hard part is removing the brown leaves without uprooting the entire plant. Maybe wait until the old parts are slimy & (eww) easier to pick off. By this time with mine I think I had 2 types of algae...better luck, better hairgrass or better ferts? I hope you win!
I don't want to discourage you but my myrios always had naked lower stems & happy tops. Just let them have long bare stems behind other stuff. If you cut them back to good growth they'll likely be too low for optimum light. Just my experience.
I'm letting the brown emersed stems melt off naturally and the snails to eat those. Not gonna uproot them and stress them out. Why poke the sleeping bear there lol
As for the myrio, thus far even the bottom leaves are staying intact, I've only had 1 stem melt at all, so that's a win thus far too.
But I know some plants don't like to be trimmed. I'm going to let it grow significantly before I trim it, to prevent it being too short. If possible I would love to fill the back corner with the plant. It's so lovely.
I kill cabomba so I'm super happy to have such a pretty fluffy plant actually living for me. I do have limnophila sessiliflora though too, which is also a nice easy fluffy plant. I'd love to find limnophila indica, its very very soft and fluffy too lol
I do get minimal algae, but the number of plants in this tank doesn't allow it to thrive much. I get cladophora, staghorn, and then green spot algae on the glass, but I use a scraper blade on the front glass, I leave the backs and sides. This tank I don't want much algae in, it's not exactly a "naturalized" scape. I removed most the wood because it was an algae magnet. My other more natural inspired tanks I embrace algae. In fact I love cladophora on my hardscape in those because it's again a fluffy soft algae.
Lol can you tell I love fluffy things?
Cladophora in my other tanks:


Same type of algae as those moss balls lol I love it in my 20g because it grows short and dense, makes fantastic "carpet" material. Grows long and flowy in my coldwater 55g though. I pull/trim it when it gets too long though.