Nereid,
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The general class of test that this proposed experiment belongs to is called, I think, tests of Lorentz invariance, or tests designed to detect and/or measure Lorentz violation.
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I don't think you could call it a Lorentz violation because in this case light would still be moving at a constant rate relative to the aether at 300,000 km per second up down and sideways. Instead, I believe it would be a violation of Special Relativity since Einstein asserted that there was no aether, therefore the speed of light should be constant in all directions including here on earth.
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I would like to ask what literature searches you undertook, to ascertain what experiments have been conducted, since Michelson's famous one, to test Lorentz violations, particularly the kind your 'pushing theory of gravity' predicts (crudely, anisotropy in the speed of light)?
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That's a good question. There are a lot of investigators out there at this time looking at such possibilities. I'm not aware of what tests have been conducted in the past. Because my collective theories could essentially be called ramifications of an aether theory, it also makes the prediction that there will always be variable aether gravity currents with unpredictable causes. Through my readings I am aware of several sources working on apparent inconsistencies right now considering flaws with these formulations.
It seems to me Special Relativity would be the first to fall since it is not an aether theory. Lorenz, if he were alive today, might argue that such variances have nothing to do with his reference frame transforms, instead it would have to do with inconsistent variable conditions of the aether field. This is also my position. My prediction as to the speed of light would be related to the unknown aether souse as being the cause of gravity if a positive result were detected.
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What experiments did you find, from your literature search?
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The only one that I can recall offhand was related to rotations of moving bodies relative to motions in our galaxy. Because of my theory of aether, I'm surprised that these types of claims were not observed and predicted long ago. The problem I'm thinking is that they will find no consistency to the inconsistencies they have observed so they will be reluctant to publish, if that makes sense to you.
respectfully, forrest