The main issue I see is algae, and nutrients.
Swords are heavy feeders, mainly via the roots. Soil has to have nutrients added to it at some point. Fish foods and fish waste help achieve this but in single jars, where will the nutrients come from? A shallow old aquarium, say a 20g long, would work better. You could plant in soil, and add liquid fertilizers as needed.
And watch the light. A 4-foot T8 tube emits a lot of light. With minimal nutrients, algae will have a field day. And you know what that means.
I grow out swords (daughter plants from my large Echinodorus bleherae which is what you have) in my 20g new fish tank. I QT new fish acquisitions in this tank, but for most of the year it is without fish. The plants thrive, somewhat to my amazement. I dose liquid ferts same as my display tanks, Flourish Comp once a week (now), and Flourish Trace. [Plants did fine before I started the Trace.] This 20g tall has two 10w Daylight CFL bulbs. I have never had algae issues in this tank, also somewhat surprising to me.
Byron.