My suspicions about the tailstock proved to be true. It was quite stuck but judicious application of the arbor press sorted that out in relatively short order. I didn't have time to clean it up or reassemble it yet. However, since I managed to get it all apart without breaking anything I'm confident it will work fine when it is all back together.

The document I have mentions that the live center is mounted eccentrically in the tailstock cylinder. It was neat to get it apart and see it with my own eyes. Nice bit of fabrication, that. Also, who knew that the live center would just unscrew from the front of the cylinder like that? I never did figure out how to get the plastic piston off the central shaft -- the fastener that holds it on there does not have wrench flats and won't accept a hex key. I scratched my head over it for a bit and then decided to work around it.

With the tailstock off, it looks to be much easier to detach the tool turret, which I need to do in order to finish tearing down the x-axis.

Photos of the disassembled tailstock are attached for the curious.