I would make sure that the bases and rings are tight before changing anything. My Ruger MKII .270 shoots very well. With almost all of my rifles, I pillar bed in Acraglas, free float the barrel, adjust the trigger and test. If it won't shoot well then, something is almost certain to be amiss with the scope.
Just a few tips on scope mounting. I lap bottom half of the rings, optically center the scope, mount securely, bore sight and test fire. Of course as Ruger rings have no adjustment, lapping and bore sighting is the only choice except shimming. I have never had a problem zeroing a Ruger rifle with Ruger rings and they are very secure. It does pay to buy a proper screwdriver tip from Brownell's to fit the attachment screws.
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