what a shame. If it was my home, I would screw the spindels into the tread of the stairs. you did not mention how they were fastened to the underside of the Banister or hand rail.
I would get my cordless screw gun and insert a drill with countersink combination. Go up about 3/4 inch and angle the drill at about a 60 degree angle and drill the hole into the base of the spindel and then into the tread. Then counter sink the hole just enough to hide the screw head. I would use a galvanized screw and the drill bit should be alittle smaller in dia than the screw.
Send the screw down into the countersink just enough to cover it. Then apply a paintable/stainable wood filler, when dry sand it off.