Brian that seems very odd. Have you checked for swarf in the moving parts and burrs on the barrel / Pinole (WTH is a pinole anyway?) along the groove where the grubscrew 404 locate?
Is the pinch bolt 4054 backed off? ISTR it had to be set just right for things to work smoothly. Too loose and the barrel flops about the place. Too tight and the barrel will not move. Needs to be set so there is just a bit of drag perceptible.
It's hard to see how a loose fitting bushing 408 would make the whole tailstock floppy. The barrel should be guided by its fit in the hole in the casting, regardles of whether the bushing is even in place or not. And when installed, the grubscrew should hold the bushing in one place and not allow any slopping about.
If that bushing is designed to rotate with the spindle, I would make the new one out of steel so the grub screw does not wear it quicklly. But if the bushing stays still and the shaft rotates inside it, brass might be better.