There's still about a foot of play in the middle.
I put wood glue and finish nails in the loose spindles but very little improvement made. Both newell post are solid.
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The spindles provide virtually no side-to-side strength; they're all to carry vertical loads. So, improving their attachment won't help at all.
You have two choices:
Install a stronger rail that won't flex as much. This could be a thicker rail, or perhaps an additional strengthening piece added to the bottom.
As @bib suggested, support the rail in the center with a second newel post, well-anchored at the base.
Of course, it's been this way since it was built, and sounds like it's a safety hazard. Talk to the builder?