The wiki states that celestial gravitation is the cause of changes to perceived gravity, so to match observations attributed to celestial gravitation it must meet these criteria.
1 Is significantly lower across the equator.
2 The overall force lines are parallel to the earth's surface so are from a very distant object or uniform object.
3 The force increases with inverse square law.
4 Celestial gravitation speeds up time, taken from observations of time dilation on mountains.
5 Makes objects weigh more while travelling west than east.
6 The source is getting no closer to the earth over time.

Does FET have any explanation of how these match celestial gravitation?
We generally accept evidence from all  sources.

The only evidence for Round Earth celestial accuracy (assuming that timeanddate is even based on RET) is the evidence you collected with your friends last month?