I do not have a bushing type sizer die, I do have a few expensive seating dies. The good news! Redding, the manufacture will repair or replace your die, If I had a rule about these things it would sound something like “it went in from the bottom, therefore, it has to exit the same way. All of my dies are versatile dies.
I have rifle friendly drifts and punches, on occasion I have found it necessary to pull out rather than drive out, something like “Depends on which side the hammer is on”. Then there is the sudden stop like the inertia bullet puller or the sudden acceleration technique, careful with dints and upsetting the metal.