Why would a plumeria rot from the center of the plant, where the three-tips formed? I have never seen this happen.
If it were my plant, I would certainly cut it below that three-tip rotting area and let that main "trunk" grow a new tip, or probably branch. You might have success in rooting that longest tip, but less success with the other two tips. This is just my experience, Cheryl.
Hetty, do you know a lady named "Denise"? She grows lots of plumeria in your area.