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No problem using the Lee, once started in the flared bit the bullet is forced down parallel by the seating die and the neck holds it tight. I dont believe It will squeeze the bullet smaller and...

As an aside the expander in the 30 m1 carbine set will do the business as well so if you happen to have a set your sorted. Not many m1 carbine bolt actions I'm picking but I have heard of a ruger...

A case flaring tool is what you are after. Lee used to make one that did from 30 to 45 cal, they might still do.
Another trick that i have employed is to deprime and reprime cases without resizing...