mwal689,
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OK. You haven't said specifically, but confirm that your headstock has babbit spindle bearings. In which case the model number is H42.
On the meaning of the "S" suffix, we still have no real clues. About all that I can say is that it appears on both Atlas and Craftsman machines from around 1936, so it doesn't mean "Sears". It seems to have stopped in 1940 on the 10" and in 1945 on the 12". Beyond that, we haven't a clue. Your headstock should have an oval instead of rectangular switch plate on the front of the headstock.
You can somewhat evaluate the amount of wear on the spindle bearings by slackening the belts, removing the motor belt, and carefully removing the bearing caps. There should be a shim pack under each end of the caps. From the factory, the pack was 0.010" thick. They were each made up of five 0.002" shims laminated together. Any edition of the Atlas MOLO (Manual Of Lathe Operation) up through 1953 (all will say Copyright 1937 on the Copyright page) gives the adjustment procedure. If the spindle is too loose, you can peel off 0.002" at a time.
You can somewhat evaluate bed wear with a 0-1 micrometer. Measure the thickness of both ways near the right end of the bed where there should be no visible signs of wear. From the factory, the original thickness was a nominal 0.375". Use the actual figure as you baseline. Measure the actual thickness of the front and rear way about every 6" from the right end up to about 3" from the headstock. Then measure the width of the front and rear way in the same pattern.