South Bend wants Type A oil for spindle bearings--10-wt Spindle Oil (Vactra, etc.)--for the reasons mentioned above.
$275 for a spindle and bearings that will at least work is a good deal. You'll need to adjust the shim stack all over again--don't run it if it's too tight when you assemble it, using the test provided by the manufacturer (and the South Bend deflection test is probably good enough for that if there isn't any period-relevant information from other sources).
The current bearings are probably worn to the point where reducing the shim stack just clamps the spindle top to bottom, and still leaves gaps at the sides where the cap rests on the headstock. That will let those oil channels on the side empty.
The openings in the new bearing caps don't have a metering hole the way the old ones do, so you'll probably want a felt plug in that opening to meter the oil into the bearing. And I'd probably replace those Gits oilers with something bigger, if they empty during a session even after you replace the spindle. South Bend uses a capillary wick to pull oil up from a reservoir below the spindle, which gives you an idea of how slowly the oil can move and still be effective.
Rick "bearings can be loose, up to a point, but they can't run dry" Denney
