It might be time for a beheading. If you want, you can restart this plant from a short-stemmed cutting (like the top half). This would be a good time of year to make the move, given your situation. Basically you would be restarting the clock, and giving yourself a couple more years of stability.
If you make this move, keep the bottom part as it will most likely branch at the site of the cut. Cut cleanly across the stem. Remove the lower leaves from the rosette (only the ones that release easily with a gentle tug). Leave it somewhere bright and cool, with good air flow, to heal for a week or so. Then set it up in a pot about the size of the original one with new soil (using fast draining soil of about 50% perlite/pumice/equivalent) and wait another week to water for the first time. Bury just the little nub of exposed stem, no part of any of the leaves.
There will be a period of weeks afterward when the cutting will look increasingly sad, probably turn brown. You should keep it somewhere bright but protected, where it doesn't experience midday sun, while it's in a funk. Avoid overwatering and avoid soaking rain. Then a month or so in you will start to see it reinflate and regain its succulence, return to green, start making new leaves. At that point you can begin to gradually give it more exposure, up to about half a day of sun probably to be safe. And at that point it will tolerate rain much better.
As a general note regarding stemmy plants, a certain amount of this is normal and expected (depending on the particular plant), a certain amount of it can be avoided or minimized by providing strong light. Overwintering complicates this situation and I am sympathetic to the limitations imposed by climate.
