Hey;
Yep; Frankenlathe. Rather odd in a way, to go to so much trouble. It seems that either these parts came from another Logan in a complete bunch, or there was some specific purpose in mind for this extreme level of modification. Otherwise, why not just get the right stuff? Not like it isn't plentiful. maybe it wasn't then? The rear of your case has definitely been machined for a more precise fit, and to get preload for that taper bearing. As Chuck says, if it works, go with it, or get a used loaded head stock (like I did) for parts.
What serial number is yours? By the case I see it is post 1943. Be advised that some time after my earlier version (1942 #15235) there was a change in the cone and cone gear. you need to make sure you have a matched pair, as they will not interchange. The ID is the same (using the same spindle), but the Oilite bushing and the shoulder OD and cone ID are quite different. Both spindles measure 12-7/16 in length.
Pic 1 - Milling the back of the case for a possible future preload setup.
Pic 2 - Before I started. Kind of obvious why I needed parts, eh?
Pic 3 - Spindle exploded.
Pic 4 - Late and early cone gears.