I didn't wrap my inner tubing and mine works great... but if you wish to wrap yours i would use 14 gauge wire as it is easy to work with and will break up the water over the whole length just fine. 12 will work if you have it, but will be more difficult to keep in place while soldering.
I'm no expert but if you see and smell no signs of infection I would prepare to bottle it, sample and bottle if it tastes good. I have done some months long secondary amd tertiary ferments in the past with good results