264.
Sounds like that .270 needs some work. Like any rifle it may need some adjustment, in the bedding, sights, or load, copper build-up. I have one that will not shot Power Pts(factory). In another .270 it will shoot Power Pts. out of the same box in a small group. Do tell! If it does not do the job for you, sell it.
Had a 7 Mag. that would not shoot exceptable groups with Rem, Fed, or Win. factory ammo. Not a happy day with a new rifle. I noted that all the factory rounds appeared to have powder charges that did not fill the case. I then selected a Remington bullet, H4831, and loads that more closely filled the case. Suddenly I had a rifle that I was happy with. I have seen Remington factory 7 Mag. do an outstanding job in a friend's rifle.
As for neck shots, most rounds from the .300 Sav. up will cause lots of damage and a large hole. I was amazed what a 150 grain Remington Bronze Pt. from a .300 Savage did to a deers neck. That is the nature of softpoint bullets when they hit the spine(hard object.)
Practice is a key element.
Siskiyou