@JDCentralFlorida, welcome to NGA. You can literally transplant plumeria anytime of year. If you are very careful when removing the root-ball/potting media, disturbing the roots as little as possible, there won't even be a transplant shock period.
When it comes to branches/tips that are growing horizontally, rather than vertically, you can do one of three things to deal with it.
Of course, the first thing is to simply let it grow the way it's growing. It will be unbalanced and not too esthetic growing that way, but it's a personal preference.
The second thing you can do is to redirect that growth to a more upward path by using garden tape or soft wire. Go ahead and re-pot that plant into the largest pot you can manage, and add a 2-3' (stiff) stake to the side opposite that horizontal branch. You can punch a hole in the pot adjacent to that stake, and simply use a twist wire to attach it to the pot. That way, the stake won't move. Then, tie the tape or soft wire a few inches below the tip and gently pull the tip towards that stake, attaching the tape/soft wire near the top of the stake. Every month or so, tighten that tape/soft wire to the stake, slowly but surely uprighting that branch. I do this all the time. I call it "training my plumeria to grow in the direction that I wish".
The third way to deal with this branch is to cut it right where it attaches to the "trunk" and then root that cutting. This is still a good time to root cuttings, while plumeria are in their growth cycle.
