Reb,
I'm assuming the bullet was in the throat area of the barrel. It most likely would be impossible to chamber another round with the bullet in the throat area. For hunting ammo I use standard dies which will squeeze the neck enough to provide plenty of grip on the bullet. I can't say the same for target loads I like them loose. Like you said, you might want to seat them deeper to eliminate the bullet leaving the cartridge before it's time.

Rem. 222