Sounds like the bullet wasn't aligned straight for seating. Pull the bullets, empty the powder, CAREFULLY de-prime the case and neck size the cases again. You MAY need to anneal the case necks to assure proper sizing. After you have done all this, make sure your bullets are straight and that your case is properly seated in the holder before you ram the bullet seater.

As far as the cases for your .270 not chambering, are they once fired from your rifle and you neck sized or were they from someone else and you neck sized? If they were from someone else's rifle, you will need to full length size and then fireform to YOUR chamber dimensions before you can neck size. Especially if you have a really tight chamber.