Normally I would recommend trying different bullet weights because different rifles prefer different weight bullets, but 130 grain factory ammo should have a higher velocity than the 140 and 150 grain alternatives for a .270 and that velocity should definiately be stabilizing the factory ammo with a 1:10 twist.
I suspect you have a barrel problem.
You might check the twist to see if the rifling is 1:10 twist that the specs say it should be but even if the twist is in spec, you still could have a problem with your barrel.
I would photograph the keyholes and attach the pictures to your note to Savage. Their website makes that easy to do.
The one time I sent data to them to document a problem and ask for advice, they had me ship the rifle back to them and they took care of the problem.
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