It is a lovely plant. The color and the obesity are a nice pillowy combination.
I think a fresh start will improve things. Maybe in spring. There is something rejuvenating about restarting plants in this group from short stemmed cuttings, maybe also there is some benefit in the fresh soil that comes as a part of that process.
I have no experience with artificial light but we do have a thread on the subject:
The thread "Artificial light for cacti and other succulents" in
Cactus and Succulents forum
As for timing, I would think a stem like yours (cutting at the point where the color changes) would root and put out new growth within 2-3 months, given permissive conditions. I mean, this is based on my outdoor zone 11 experience in a climate pretty much ideal for these plants. It will double in height in less than 6 months, closer to 3 months. That is my propagation cycle (when the next beheading will occur and half the plant will go to starting a new one). If I were to propagate from leaves I would achieve greater numbers (with an initial lag of a few months) but really I have no need for dozens of these right now.
These plants seem to flower pretty freely once they are a certain size/age, and not sooner. One of my Pachyphytums flowers every few months sort of sporadically in an 8 inch pot (at least twice a year, usually with multiples) and the other one (pictured) has only just now started flowering in a 10 inch pot. It doesn't take that long. The plant pictured came to me as a single small head a little more than 2 years ago. In the meantime after serial beheadings (straight up multiplication) I let my first decapitated threefer go unmolested, and that is the result. I suspect by 5 years they would begin to approach senescence.
Again, speaking from the perspective of very permissive conditions. Plants in habitat would live much longer but they would also be a lot scrappier, with much smaller leaves and rosettes.
There does seem to be an effect where limiting pot size begins to shrink the rosettes, and allowing a bit of extra space tends to make them bigger and fuller. You kind of have to ride the wave there and let the plant tell you when it might like more space. Your plant would definitely enjoy more space once it has rooted and properly filled out a container.
