Sean,
One of the problems with Atlas Illustrated Parts Lists is that the ID of parts like collars and washers is more often than not drawn either too large or too small, making it impossible to determine with confidence what part they fit over. The back gear subassembly drawing is a good bad example (although not the worst I've seen, by a long shot). I do not have either a 10" or an early 12" headstock here to pull the back gears off of and figure this out. So if you have not already done so, please go to DOWNLOADS and download the file Craftsman Lathe 12 101-27430_27440 12X24-36 Rev5.PDF. It is at the moment at the top of the list of some 2000 files because I just updated it. So you won't have to bother with drilling down to the Atlas level to find it. The scan of that document is a little better quality than the otherwise identical one in the 101.07403 parts manual. Go to file page 5 and look at the back gear assembly at the top of the page.
Tell me whether the ID of the 10-167 Wave or Crinkle Washers and the 10-253 Collars are large enough to fit over the 10-251 and 10-252 Eccentrics. In the drawing, their ID is too small. But logic says that they should be large enough. If their ID's fit over the eccentrics, then selective positioning of the collars will allow shifting the two eccentrics (and the back gears) a little bit left or right. Shift to the left will be limited by the 10-254 Handle hitting the 10-245R Bracket.
Ideally, the back gears should have about 0.004" end float between the two eccentrics. If it is significantly more than that (say greater than about 0.008"), purchase some bearing shims in the proper thickness to reduce the end float to 0.004". And as I wrote earlier, you can also shift the pulley and gears on the spindle slightly left or right if necessary. Finally, when you have everything else right, loosen the set screw in the left 10-253 collar, flatten the Crinkle washer slightly, and re-tighten the set screw. Repeat for the right ones. This puts some friction drag on rotating the two eccentrics and will prevent them from vibrating out of (or much worse into) gear engagement while the lathe is running.