How to tighten a wobbly stair bannister? I tried going in from the basement ceiling, the floor boards are in the way. I tried drilling in a screw at an angle at the base to anchor to the bottom stair, and lets just say I now need to figure out how to extract a broken screw and patch a hole to lessen the carnage. I imagined there is a nut/screw job under the wood that needs to be tightened, but darned if I can figure out how to get to it without ripping up the wood. I could try some glue, I suppose, there is a tiny gap around the bottom, but that doesn't seem like it would last past a few pulls.
I guess you already know that your attempted fix is a fail. One realistic way that such a newel post can be made more sturdy would be to do some re-work to the structure as follows:
A flat metal bracket is made with a round metal post welded to it. The round post (0.75 to 1.0 inches diameter recommended) would extend up through a round hole in the lower stair tread and rise up to a height of 10 -> 12 inches. The metal base plate is screwed up to the bottom side of the stair tread. The center core of the newel post would then be bored out to permit the newel post to be mounted on the projecting round post. (See picture below).
This is a tough repair to do without taking your entire balustrade apart.
Try to remove the bullnose riser. This might give you an opportunity to tighten up the newel post from below. (Long screws, glue, whatever you can think of...)
If this doesn't work, something like a Zipbolt (eg ZB 10800 UT MINI) might do the job, though this would entail pulling (possibly cutting) the bottom of the newel post away from the tread in order to drill the newel and tread.
This is likely a factory made bullnose riser, because it is round. It will have a bottom and a top firmly glued into the round part of the riser assembly. The idea is to install a 1" dowell up into the newel and down through the tread, the riser top, the riser bottom, and even on through the floor. Your installer skipped that step. And there's a broken screw that has forced a space between tread and newel. IMO there is no way to fix this. Consider buying a new newel. Buy one with a square base. Paint in contrasting color since you cant match the stain. Remove the tread. Next make absolutely sure the carriages and riser assembly are bombproof strong. Everything else you will do depends on it. Install blocking between the carriages. Then build up the inside of the riser assembly solid with layers of wood, screw and glue layers, attach the risers very well to the blocking. Then glue and screw the tread back down on your bombproof carriages and riser. Once again, bombproof. All the strength will depend on it not moving. With your new newel buy a newell mounting kit. It is 1/4 inch plate steel about 4 3/4 x 4 3/4 with holes drilled in it and 4 pieces of special trim to cover. Screw the plate to your newel. You will notice the plate sticks out about a half inch all the way around the newel and has exposed holes. Screw the newel to the tread. Cover the plate with the special trim. I always prefer the oak dwell connection, but it is not always possible. When forced to use another method, I have had good luck with these mounting kits.