I have a 9" South Bend lathe (the one the Sabel machines were patterned after) and have had my spindle out to rework a few issues. Your lathe looks VERY similar to my South Bend.
The spindle on my South Bend is "superfinished" steel and it runs directly in the cast iron headstock bearings. My lathe appears to have only been oiled, no one ever greased it as far as I can see. Superfinishing is still done today for some parts, it is a special honing process done after precision grinding the spindle, to further improve its' roundness straightness and finish. Some cams and diesel fuel injectors are still made this way (or were until recently) in North America. Anyway, I would not let anyone loose with a grinder on the superfinished spindle of your lathe unless it shows blatant damage, ie scores or galling. In my lathe I did find a number of high spots in the headstock bearing (as Hopper mentioned to look for) and also a few artifacts that looked like chunks of swarf that got jammed in the bearing and gradually wore down. Despite these problems in the headstock bearings the spindle was very good, and I only stoned a couple of "dings" down with a 2000 grit stone and oil. In the headstock bearing next to the chuck I very carefully removed the chunks I mentioned and cleaned up the high spots with a riffler file and followed it up with fine stoning. after a thorough cleanup and wash-out I rechecked it with blue and it looked and felt much better. I'd recommend a very close exam of your headstock bearings. If they're all chewed up, fine, you could get them bored and bronze bushed. If they're mostly OK looking and smooth, I'd look for artifacts that don't belong there, clean them up like I did, and then adjust shims. At the far end as you did I added a needle brg and ground thick washer thrust takeup system. These mods transformed the lathe, it now has far better finish, no odd headstock brg noises under heavy loads, and no more "ticka ticka ticka" noise from that thrust end when drilling. I did not change the headstock shim packs on my lathe at all. With the shims on your lathe I would sneak up on them. If the original pack of shims is gone, take out all the shims and fit the spindle. Note if there is any up/down back/front spindle play, and how much of each, with a DTI. (if there is more than about .003" of free play up/down front/back the brgs / spindle may be too far gone, and rebuild may be needed, but try shimming as below first.) Measure the stack gap with feeler gauges (make sure the gap is clean first.) Then put a shim stack in that is about .0005" less than the measured gap also less the max play you measured. The headstock bolts can then be tightened gradually checking every 1/8 turn for spindle free movement. The bolts should not need to compress the headstock bearing overhang more than .005" or so or you risk breaking off the bearing overhang in the casting and scrapping the headstock if you do, so go easy and sneak up on it. This is NOT a job to do if you are tired, angry, or in a rambunctious mood. Care is needed. Add or remove shims in .0005" increments until the spindle runs free but with virtually no up/down back/front play.
After you get to that state, use only ISO 32 grade hydraulic jack oil in the bearings and mechanisms of the lathe. That is what South Bend recommended originally and it has worked great for over 25 years in my lathe. Grease is not recommended.
If you can't get it to that state, you may need to have the headstock bushed by an experienced machine tool rebuilder. Again though unless the superfinished spindle bearings are scored, grooved up or otherwise trashed, don't let anyone grind them.
Hope the above is useful.
Now waiting for the usual 15 armchair experts on the forum to tell us it's all wrong. Well, all I can say is it worked for me and was based on South Bend's recommended practices. My lathe works great.