Some thoughts
Measure the diameter of the cylindrical register on the div head and on the Lathe and compare.
Also check the inside diameter of the register on the griptrue. This will tell you how much "slop" you could get if the threads are not concentric or are mucky.
There does have to be some clearence otherwise the chuch will not screw on so it's the thread that does the centering with the register acting as a solid limit.
Have a really good clean up of the threads and as others have said check for any sign of bruising.
regards Martin