How much run out are you getting?
As a side note, I have seen the locking rings on a set of dies I have cause runout, The ring was not faced off square to the threads and when you tighten it down in the press it would push all the slop in the thread to one side causing the die to cock. This was finger tight in the press but I went with another locking ring and all was good. To prove it was the ring, I marked the cases so I could index them and sized them and check the runout against the index mark. Then I took a piece of paper and put a small piece between the press and locking ring on the low side. I resized another marked case and my runout was cut so I added a second piece of paper shim and tried it again, my runout was gone.
Some of the old lock rings that used set screws that impinged on the die body threads were bad for cocking the lock ring, see if your run out reduces by fully floating the die, lock ring backed off. Long term, if that is a cause, buy Forster clamp style lock rings.
