Best not to use clear cups IMO. This will encourage algae growth and fungus gnats.
So how about you 1) put a small paper bag around the cup so light doesn't get it, 2) stop feeding with nutes, and 3) water the moment the top gets dry? OR replant into a larger container, even if it's one of those one gallon, 6 inch pots?
If that is just straight peat moss you should 4) throw in something for aeration, like pumice, perlite, or untreated mulch. Even a 1:5 ratio would do it. That way you can get the roots wet more often (which is good) without having them actually sitting in water (which is bad).
Just a note on using fertilizer. Every time you feed, the chemicals you put in get absorbed into the media. The root system of a plant must be
dense and healthy for nutrients to be taken back out of that soil and into the plant quickly. When using fertilizer there is a point before the point of burning the plant where it doesn't need to grow more roots to search out nutrients, and hitting this point can be a cause of slow plant growth because of slow root growth.