I had a USRAC push feed Featherweight in .270 that had similar problems. The barrel was not free floated, and had un-even pressure against it. I free floated the barrel, and that helped slightly. It reduced the stringing and made more consistent "round" groups. Group size, however, only slightly improved. Next I tried the old credit card under the forearm trick (about 2 inches back). This magic number was 2 cards thickness. Groups shrank from about 2 inches to about 1 to 1 1/4 with loads it liked. I epoxied the cards in place and called it good. Provided the recoil lug / bottom of the action and tang seem to be making proper contact, I would try the above first.
Larry