I think Tony's spindle is 13-23/32" (if I read that right). That is only a 1/32" shorter than yours. The length is the least critical dimension. The collet draw bar can easily span that difference. Both lathes have the larger spindle (the spindle hole is listed as 1-3/8" which is the larger spindle).
I'm curious about the electrical controls on Bill's lathe. The card indicates that it has a non reversible motor starter. The "West DE-10N MTR. 10-100 Watchman Style" doesn't imply anything to me. If it still has the original motor and controls, it would be interesting to know what they are and may shed light on the meaning of the description on the serial number card.
