MG-42,
Please don't cram a .323" bullet into a .308" swage die. Swage dies, as you know, employ opposing punches that squash the contents of the die and cause those contents to take on the shape of the die bore and punch ends. Some springback is helpful once the contents are placed under a pressure load and then released from that load in allowing the newly formed slug to be successfully ejected from the die. A lubricant that does not detonate under pressure, like lanolin based stuff, is also extremely helpful.
If you stick a bullet in your die you will be very unhappy because it will be nearly impossible to dislodge without destroying the expensive die. Even then, the excessive pressure that was possibly exerted upon the die walls may have expanded these normally nearly perfectly straight walls to the point where they are now "barrel" shaped (that is small on the ends and fat in the middle) and not able to produce a properly formed bullet.
Diameter reducing dies are available for making bigger bullets smaller, but if you want to put a special tail on a .311 or .323 jacket with seated core, by all means purchase the correct dies for this purpose.
Swage up. Size down.
Hope I didn't offend you.
Paul