I've found that adding floating plants really helps with new tanks and just about everything else. Plants can directly take up ammonia and nitrite as well as nitrates, from what I've read. Floating plants like Amazon Frogbit are especially good at this because their growth isn't limited by lack of CO2 (in the case of aquariums that don't have CO2 supplementation). I keep floating plants in all of my tanks and they do a really good job of keeping the water parameters and occupants happy. I also believe that heavily planting a tank helps prevent ich - I've thrown fish from just about everywhere directly into my tanks and I haven't experienced a single ich outbreak. I've had fish die of course, but no outbreaks that spread to my existing fish. That could just be dumb luck too of course...
So my advice is to add some amazon frogbit
It's easier to remove than duckweed and every time you toss some out, you're throwing away all sorts of stuff that the plants have sucked out of the water - a win for all! Of course the more light over the tank the better it grows, but it also helps out-compete algae to keep your glass cleaner.