Did they make the post-64 push feed in a short action, or did they merely block the magazine? If it is a true short action, that would be a low-cost way to go. The CRF of the Classic action is probably of little value in the build you are envisioning.
Yes, and they're not uncommon. For example, Rangers, early Featherweights, Stealths and HBV's in 308, 243, 22-250, etc. all used push-feed short actions.
