Gorgeous plant!! Congratulations on getting it to bloom and thrive in your area.
If it were my plant I would try and keep it in one piece and overwinter it barerooted in a frostfree place. Plumeria go dormant in the winter and need neither light nor water during this time, they just need to be protected from frost.
If you decide to trim I would take three cuttings, leaving appr. 6-8 inches of stalk from which new branches will eventually emerge. You should know that you most likely won't get blooms on those new branches until the year after next. So - it's a big commitment!
Edited to add: I think that is a 'Celadine', the most common flower in Hawaii for leis. It has an outstanding fragrance, as well as great keeping quality.
