Okay, I think I have this figured out:

My spine was a spline IK whose curve was smooth bound to some floating joints, which I parented to controllers so I could tug on the spine. By itself, the joints can be moved wherever without stretching my bound bones, they just conform to as much of the curve as they can cover.

The reason my topmost joint was stuck in place: the neck has its OWN spline curve with some bound joints. The joint that was anchoring the bottom of my neck spline in place was parented to the chest controller, so it forced my neck bone to go wherever that controller went instead of obeying the curve.

I fixed it by parenting the neck spline's anchor joint to my spine driver chain's topmost joint. Now it follows the spine curve without stretching.