Clayton,
Measure the taper angle between the head and the straight cylindrical body. If it is 12 deg., the collet was supposed to be a 3C. Or at least the threads, body diameter and head angle would match the 3C. So a 3C would fit the spindle nose adapter or closer if the head angle is 12 deg. You might have to adjust the thickness of the thrust washer on the back end of the draw tube (the straight sided one, not the tapered one). You might also be able to adjust the spacer to fit 1AT but I do not know what the head angle is on the 1AT. Neither Andy's list nor two other ones that I have give the head angle. Plus the 3C is much easier to find. The 3AT is standard on the Atlas. But it is is too large in diameter (0.687") and has a 15 deg. taper. Unless the collet that you have is a sloppy fit in the adapter but has a 15 deg. taper.
Both the 3C and the 3AT have about 16 threads. The proper effective length of the draw tube (with spacer(s) ) is that it should take about 8 turns to screw up onto and tighten the collet.
Robert D.