Funny how you said the math is never presented, then instead of addressing the observation directly, you start pointing to other examples and making misdirection claims instead of addressing the fact that the observations don't match the claimed rate of curvature.
Discussion
Without the having the actual spread sheet this is about the best that I can respond.
Bennett's formula calculates refraction for light from distant celestial bodies (e.g., stars, the Sun) entering the atmosphere at high altitudes.
Terrestrial theodolite measurements (e.g., sighting distant peaks) require a different refraction coefficient due to localized atmospheric effects near Earth's surface, such as temperature gradients and pressure variations
Can you justify the use of Bennett’s formula considering it was not designed for this use case?
The difference with or without a correction for refraction is basically negligible. At most you are looking at 7-10% that can be attributed to refraction, which cannot fulfil the requirements for explaining the discrepancies in the results, because it is too large.
That's the last pillar of the defence for long distance observations, and refraction isn't enough. You can observe silhouettes of maintains over even longer distances which cannot be attributed to refraction at all.