Here's the Deal:
Live primers can be removed from a cartridge case by using very, very slow and gentle pressure on the operating lever of a standard single-stage reloading press/depriming-case sizing die setup. (Pretty much like removing a spent primer, only much slower and more carefully.)
Notice I clearly didn't say "safely removed." Just "removed".
Having said the above, I'll further say that most of my unnecessary bodily injuries incurred during reloading were caused by injudicious messing around with primers. (But not all injuries: I've managed to run the depriming/ decapping pin through my fingers a coupla times, as well.)
Now, here's maybe a better alternative if all you want is to seat the primers deeper (properly). If the bullets have been pulled and the powder was dumped out of the case, then the primers can be seated deeper (flush or even below the case head) with about the same degree of safety as any other hand priming. Remember how the primers got into the case in the first place: Squeezed/seated in with a hand priming tool, most likely. If the primers in the cases are not so high that they won't go into the hand priming tool at all, then they can be reseated deeper, as just stated.
Just remember to always keep the open end of the cartridge case pointed in a safe direction away from your person in the event of a primer pop-off. Just like regular hand priming. FWIW, I point the cartridge cases into a bucket while hand-priming. Because primers have the energy of a medium-sized firecracker.
A primed .223 cartridge case is worth what.............25 cents?? (Primer + cartridge case).
Pitching out the mistakes is always an option worth considering.
FWIW,