I am not well versed about "full water culture", but here's my take on the scenario you described:
By submerging the roots, you have likely suffocated them. Keeping the base of the plant submerged is not going to help, and can hurt.
As roots grow, they "tailor" themselves on a microscopic level to the environment they're in, so they can function optimally. Once they have grown, that tissue cannot change.
Those roots did not grow in water, so were - literally and figuratively - completely "out of their element" when you stuck them in water, so died. If you want the plant to survive, it must have new roots. I doesn't matter a bit how you want to grow it, but the roots must be right for those conditions.
As it is, the plant has no way to take up water (base immersion doesn't cut it), but can lose it through leaf transpiration. The challenge is keeping it from desiccating to death before new roots emerge.
You can certainly keep it in that glass container, but 1) lower the water level so there is no contact with the plant (becoming a humidity source only), and 2) invert a clear plastic bag over the plant and container, without sealing it, to simulate a greenhouse to trap the humidity. Keep it VERY warm and in deep shade, and in a few weeks you
may see new roots emerge.
Once that happens, you can repot it or leave it in the vase. If they continue growing and enter the water, that's fine, as they will be optimal for that environment.
You can accelerate the root-growth process through use of a good
stimulating formula.