Yes, if the plant can "see" the sun, that would be better. Reflected and diffused light is great indoors but it's not an good substitute for a line of sight to the sun. This plant is actually kind of needy about strong light. I don't think that dialing up the light will necessarily save your plant at this point, though it can only help, and it will probably be necessary for any rescue to be successful.
I don't think you're going to get anything useful out of unpotting the plant. If the rot is already in the stem, it will tend to progress upward until it eventually consumes everything. There's some chance that what you're seeing does not progress, so don't give up hope right away. But unpotting the plant will only damage the roots further and stress the plant out more, without solving the core problem of the rot invading the stem itself.
The best route to a rescue would be to restart the plant from a cutting taken where the stem is still solid and green. Using a sharp knife, cut straight across the stem (anywhere that it is healthy, a safe distance from the discoloration). Avoid touching the sap and especially getting it in your eyes (potent irritant), and clean your instrument carefully afterwards, while the sap is still wet. Leave the cutting in a bright place to heal for a week or two, then pot it up with just enough stem buried to provide the necessary stability. Use potting soil mixed with an equal volume of perlite/pumice/etc. as drainage is very important. Wait another week to water and then probably monthly from there until you see new growth on top.
