Andrew, in hindsight I could have done it that way on this job had I built the newel with a large tenon on the bottom. And w/o a doubt that gives the strongest connection possible. I've seen some old houses where the newel has a big round tenon on the bottom that goes through the floor and blocking below it that spans between two joists, and is held in place by a big tapered wedge through the tenon. That allows the joint to be tightened, if needed. No matter how it's done, you need a really solid connection on those unsupported newels.
John