Why blame the dies?
Your lube or the way you are using it is the problem.
All my sizing dies have come set perfectly from the factory over the last 40 years.
If yours isn't, loosen the die body and the spindle.
Size a case (you may been to jiggle the case and spindle to alignment) and WITH THE CASE IN THE DIE, tighten the spindle and the die lock ring.
If you have further alignment problems, the problem would be cases. Many cases have the flash hole off-center. Generally, the depriming pin will still slide in; however, I have to discard maybe one in 300 random cases for severly off-center flash holes.
I do not like the Hornady One-Shot in the aerosol can. I prefer Lee case lube (dissolved in water), or the Frandford Arsenal or Dillon lubes in the hand pump bottles.
Not the One Shot doesn't work, but it has a very heavy body that can build up.
Also, with ANY spray lube, you need to be sure that the cases are treated all the around and that you let the propellant/solvent flash off for a minute or two. Until the propellant and solvent are gone, the lube doesn't work very well.
Too many people won't wait and rush to start, causing them some of the problems you are having.
I prefer to de-prime off the press. When I come back from the range, I inspect, deprime, and sort all cases prior to tumbling in 20/40 corn for 30 minutes. The Lee Universal Depriming Die has worked great for about 10 years, never breaking a pin.
Unless you are loading several hundred cases at a time, you can also use a hand deprimer so you can place the pin in the flash hole yourself.