That kind of work was only $750 20yrs ago, money is worth less now.
My really worn 1951 manufacturing model has a lot of slop in the quill, but the most important thing is that the quill is in alignment with the spindle.
Almost always the quill is pointing down and toward the rear of the machine, the cause is moving the tailstock along the bedway by its handwheel.
To help reduce wear, the tailstock can be grabbed by the right hand at the back between the ways, with a couple of fingers of the left hand under the front lifting slightly. That can be done even when peck drilling, with not much loss in time.
Anyway, the tailstock is worn the quill is out of alignment, and it sucks for most uses. And because tools enter at an angle they do the wobble from the wear in the quill.
Fix it any way you want, but here is the donie path of least resistance!
Take the base of the tail stock, file the ridges from the V and flat, then scrape it a bit so it has reasonable contact with the bed. Not, trying to level the top of the base at this point, just going along with the wear. Don't try to be too critical there because you probably have bed wear as well.
Take the tailstock base and prop it up on your mill. using round rod in the V and shimming the flat on the bottom, begin fly cutting the top flat, you can remove it, and test on the lathe to adjust the shimmed flat side, so it ends up reasonably level.
Then, depending on how much material had to removed from the top of your tailstock base, will be the thickness of the shim or plate to bring the tail center back up and level.
With that done, the slop in the quill is not near the problem it was.
On the later lathes with the large quill, the tailstock has to be lubed with spindle oil, or it will be hard to move the handwheel, my old one I use way oil.