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So - Here can we observe that energy for m at h from M is not observer dependent? It cannot be observer dependent because it has observed physical consequences.Therefore the observed frequency of a caesium atomic clock's caesium atoms at h from m, or in relative motion, will have a frequency associated energy, and neither this energy, nor the observed frequency, can be considered to be observer dependent.

0h - so now you admit that the observer at 50 feet will actually observe the ball to be travelling more slowly at 50 feet, a fact that will also be noticed by the observer on the ground, as acceleration is noticeable, but you refuse to agree that the caesium atomic clock's energy at h from m is causing the higher frequency that is observed by the observer on the ground?If the cannonball has more potential energy at h from M, then so will the caesium atom..

The caesium atomic clock at h from M, held at rest with respect to the g-field, isn't experiencing a conversion of potential energy to kinetic energy.

It's exactly the same phenomenon, with the same result. Potential energy becomes kinetic energy. In the case of a mesoscopic object, it goes faster as it falls down a potential well. In the case of a photon, its frequency increases.

Obviously, but it started out with more

By rights what you suggest would ensure that the 100kg cannonball accelerates faster in free fall than the 10kg cannonball, and we know it doesn't..