I will all but guarantee improved plant growth if my suggestions are followed. I have seen this too often in my 30 years of low-tech planted tanks. I have zero GH/KH water, which of course means no calcium or magnesium. I do not add these aside from the fertilizers I use. I have lush growth from my large swords using Flourish Tabs and Flourish Comprehensive Supplement. I used to use Equilbrium (plus the liquid) to up the macros, but after a marine biologist questioned me as to the impact on fish, I stopped, and went to using the Flourish Tabs replaced every 3 months. The swords are still thriving, and that was 7 or 8 years ago.
The light was an issue here, it is not adequate and this is largely the spectrum. Removing the beneficial floating plants is not the answer. I know I consider fish first, plants second, and the floating plants definitely make the fishes' lives easier. But they should not impact the lower plants if the light is adequate, and with sufficient fertilizer/nutrients.
I will just post some photos of my tanks over the past 10 or so years, the swords do not look like they are starving or failing to me. I have heavy floating plants, zero GH, and used Flourish Tabs and Comprehensive liquid.