You didn't say what's wrong. Are the faces not parallel? Or are they conical? Or what?
From what you describe, I would expect two faces that are parallel, but each slightly conical. The face on the tail stock end should be slightly concave and the one at the headstock end should be slightly convex. This is due to the fact that no lathe can have the cross slide exactly perpendiular to the main ways and all manufacturers, well most anyway, will make sure that the error is towards a concave face where facing is normally performed, on the tail stock end. By "slightly" I mean perhaps 0.0005" or perhaps 0.001" for a part your size. If that is your problem, you will have to turn it around to face the second side.
I am doing a similar job at the present. My spacers are only one inch in diameter and vary from 1/4" to 1" long. They have a center hole which also must be concentric so a stud is out of the question. I am making about ten or so. Chasing tenths is a b***h. I'm using a shop made "collet" that grips the 1" OD. It was turned on the lathe's spindle with a flat face for the parts to seat against that is dead true (because it was turned in place). The gripping area is only 1/8" deep but it holds well enough for a light facing cut. I have to be sure that it is dead clean when mounting each part.
Probably the best way to do a piece like this would be to use a custom face plate. Give it a final truing cut when it is mounted. You can use a three or four jaw for the OD and the first face with no problems. You could rough out the second face the same way, leaving 0.010" or so for the final cut. The part is held with the first face against the face plate with a threaded rod through the spindle or with several bolts in a circle through the face plate. In either case, you will need one or more tapped holes in the part. Or a center bore and a nut in a recess. Use whatever is best for your part. Take light cuts.
This should insure that the two faces are dead parallel and also that BOTH are slightly concave.
If you need a better finish on the ends, you can use abrasives to lap them. But be careful to keep the faces parallel. If you do this under power on the lathe, it should be a very even process which would keep the faces parallel, but they will tend to become convex in the process. If you do it by hand it will be easier to keep them flat, but they may stray from parallel and frequent checks will be needed.
Of course, a surface grinder would make fast and accurate work of it. And no concave/convex. But I don't have one either.
Make it fit.
You can't win and there is a penalty for trying!