anything that grows fast is guaranteed to pick up a lot of nitrate. that being said plants that grow out of the water are best for this given the right amount of light. Pothos grows like crazy and I would put my money on it. the root system that it makes in the water is impressive.
Hornwort would be best IMO. I personally hate it but I think t would work best for what you're looking for. I would prefer it over Water Lettuce or Duckweed since it will grow below the water also so you could potentially allow it to grow much more that the latter two. Water lettuce would be my second choice since it can grow very extensive root systems.
Also, if you can get a plant called Parrots feather that grows fast and sucks lots of nutrients and is not a fussy plant. Can grow in all kinds of poor conditions. I keep some in my pond and native fish tank.
I would really be careful about Parrots feather since it is an invasive plant in many places and I personally don't like encouraging shops that imports something that could be illegal. Most shops don't know about plants being ban from importation so check your local laws. If it's cleared then go for it because it would work wonders.
Agreed Water Sprite is a nitrate sponge. Adaquate lighting and it grows so fast you'll pull bunches out every month. Pothos roots in the tank work great too let it grow down the outside of the tank.