Thanks for your good suggestions. The misalignment seems
only horizontal *so far).

Packard has a Morse Taper alignment tool (both #1 & #2)
which I will order before I do any serious lathe realignments

The Tailstock has a locking set screw but adjusting it does
not seem to do much of anything.

I did not find any setscrews holding anything (other than the
belt guard) at the headstock end of my lathe.

I will loosen the tailstock end of the monotube mount
and see if the monotube can be rotated.