Gravitational blueshift and conservation of energy

I've seen various discussions on whether conservation of energy is valid in regards to general relativity. Some say that the energy is shunted to or from the gravitational field, others say that conservation of energy does not hold when dealing with general relativity. But what really makes me confused is that people say that if gravitational redshift (and therefore gravitational blueshift) didn't exist, it would make perpetual motion machines possible by allowing one to use the weight of photons to transfer the necessary energy upwards like the balls in the famous wheel-based nonfunctional perpetuum mobile design. The thing that I'm having trouble understanding is why one theoretically couldn't use gravitational blueshift to make a perpetuum mobile, by applying a strong gravity well when a photon is emitted and then moving the well to blueshift the photon, then having the photon converted into a non-wavelength-dependent, more stable form of energy, then using the stabilized energy to emit more photons, again with the gravity well in place. Would the moving of the gravity well require as much energy as would be gained by the photons?