You could try changing larger amounts of water durring your water changes, I know smaller and more frequent water changes are better, but in reality some people for what ever reason cant. As long as the new water is similar to the old water a larger water change like 50% shouldn't stress the fish. I get my water from a well, so I don't have to remove chlorine and other chemicals. I don't try to adjust my water to match the fish's needs, instead I keep fish who's needs match my available water supply. I use a hose connected to the kitchen sink for water changes and use a thermometer to match the tap temp to the tank temp.
I suggest this because even if you get a completely overgrown jungle of fast growing plants they will remove a small amount but not all of the waste from a heavily stocked tank.
Fast growing stem plants such as Anacharis, Hornwort, Water Sprite, etc are said to be the best at removing waste. Their ability to remove waste depends on how well you meet the plants other needs such are light, CO2, minerals etc. If your looking for a way to reduce work for yourself, I'm not sure plants are the way to go, becuase with plants you have to deal with pruning, snails, algae, dieing plants and many other things.
You might be able to get away with it and reduce your work load if you have a large very lightly stocked heavily planted tank with slow growing plants. The reason for the slow growing plants is that they don't require weekly pruning to keep enough room in the tank for the fish to swim.
Just some of the thoughts that went through my head reading your post.
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