Max Born, "Einstein's Theory of Relativity, Dover Publications, 1962, 1965. Chapter VII: Einstein's General Theory of Relativity, Sub chapter; optical deductions and confirmations.

If everything was relativistic mass inflation we would not be able to detect gravitational redshift of spectral lines coming from our own sun. I think that gravitational potential as described by Born has no equivalent in GR, it is adapted from classical mechanics. IF there is gravitational potential as described by Born, THEN the energy surplus derived from this cat and made real in all reference frames by the neutrino/matter interaction mechanism does violate energy conservation. IF there is only relativistic mass inflation THEN of course you are right, SLAC does this act all the time. What SLAC does not do is create mass out of the energy difference between two points using a gravity field.