Can any of the gearing in the head driving the feed pulley be changed? There also doesn't appear to be any way of reversing the feed screw or the feed shaft (one with the belt drive). Not seeing it or missing? Never there? Are there 2 banjos? Or is one of the levers for the lead screw reverse and no gears on it?
Not sure how much end play in the spindle, but it sounds like it is fairly easy to adjust, run with no load and see how warm bearings/ caps get. Tighten end play a bit and check again with no load. Make sure oil caps have oil. Should be able to feel a small amount of play. Basicly, no load, very little to no warmth, under load (cutting etc.) slightly warm, if you can't hold inner wrist against it, to warm. Like checking baby's milk. Please stop lathe before checking tempature.
One of the things I remember reading for how to be a good lathe/machine operator was "oil before it starts to squeak and back off the tail stock as things warm up".