After reading your message, I gave some more thought as to what I may have done wrong. The part I am seeing movement in is the bottom newel, on what is basicly a two newel system. The top newel is notched to fit over the upper floor, with the non notched portion being bolted to the frame of the floor with 3/8 inch lag bolts. This newel is very secure and I see no movement.
The bottom newel is another animal all together. It is notched (an angled cut) over the somewhat weaker framing of what used to be the plaster half wall (which I reduced in height to acommodate the handrail runner). I suspect that the 8 inch long 2x4 framing which now remains at the base, may not be very strong, and the entire assembly may be able to move left to right a bit (even though a 10' long 2x4 secures the framing studs together under the runner).
Now for my idea:
I have a basement.
I drilled a small pilot hole next to the bottom of the base newel and I have located the newel above the floor. If I attach the newel to a steel backer plate on the basement side of the floor(also bolting the steel plate to the floor joists), could this increase the stability of the newel enough to continue on? It is the only weak link.