I agree that the main thing here is probably the light. I believe you now have two 10w CFL Daylight 6500K bulbs, so that should be fine. That is what I have over my 10g and my 20g, and the plants thrive--and the 20g is plants only (no fish, it is my QT for new fish). And interestingly algae is never an issue in these tanks.
I won't argue about possible benefits of increasing the KH for the carbonate, that is something I have never bothered with. But I will say that my tanks have near-zero KH and have for 25 years. I have never raised it, except when I was using half a cup of dolomite in the filter for a time. But I didn't have a KH test back then so for all I know, that was minimal anyway. I do know that my tanks are now zero KH and the tap water is 7 ppm which is less than 1 dKH. And the plants are fine.
Your GH at 5 dGH should be sufficient. I use Equilibrium to raise mine from near-zero in the tap to 5 and 6 dGH. IF the GH were too low, you would have iron deposits on the leaves (iron replaces calcium when the latter is not available) and these are brown blotches that increase in size, killing the leaves and then the plant. A photo might pin this down, but at 5 dGH I do not expect this; my swords improved rapidly.
To the plants. If these are those in the photo, you have higher-light requiring plants. E. osiris (which is I believe what that sword is) needs more light, and nutrients. I had one that wasted away and that was in my tank with Flourite enriched substrate and slightly more light. My other swords are fine. The stem plants, Cabomba and Wisteria, need very good light. I have no luck growing either due to minimal light.
Better plant choices would be pygmy chain sword, chain sword, crypts, Brazilian Pennywort.