First off, between about 1932 and March of 1981 Atlas/Atlas-Clausing/Clausing-Atlas/Clausing Industrial made two different beds in four and then two different lengths. The two different beds had from 1932 until mid-1957 nominal 3/8" ways. From mid-1957 on the ways are a nominal 1/2" thick and in general the other dimensions are a little heavier. Second off, your statement that the apron (that is the vertical front of the carriage) and Saddle (the rest of the carriage) is not removable is incorrect. You just have to know what to remove first.
There were actually three different carriages. From 1932 until about 1938 the saddle and the apron were all in one casting.
From 1938 on the saddle and the apron were two separate pieces bolted together. And the one or two castings that fit the 3/8" bed are not the same as the two that fit the 1/2" bed.
In all cases, however, once the apron was attached to the saddle, the carriage was held to the bed by two pieces of flat-bar bolted to the bottom of the carriage or saddle. And there were shims between the retainer bars and the saddle or carriage that adjusted the vertical clearance between the ways and the bars. But in any case, neither version of the early carriage is usable with the heavier bed. So in order to put the machine back together with the newer bed, you will have to acquire a newer carriage.
It is possible that you might be able to use the early headstock and tailstock but you will have to use longer clamping bolts and most likely drill and tap the new mounting holes in the older headstock or drill new mounting holes in the newer bed. Plus probably use longer bolts. But what you should do first is to determine the model number of the original lathe.
