Clarifying the math for the curvature

We've all seen the 8in per square mile calculations and and the globe side they said "but you don't account for the height of the observer" and/or "it's not a parabola"
https://math.stackexchange.com/questions/1896238/how-to-calculate-curvature-of-earth-per-surface-kilometer

or "you don't account for the elevation of the ground itself"

Here is my question then, if I'm flying on the North American continent, at 37,000' MSL and I see a mountain peak at 400miles away technically, at 400 miles, we're obscuring 18,000 feets. There's no peaks in continental US that is higher than 18,000 feet MSL (beside Alaska and Yukon). So then would it be fair to say, according to the globers that it would be absolutely impossible for me to get a P1000 camera with an infrared filter and see any peak at 400 miles away ? Because that sounds pretty easy to prove or disprove if you fly long enough to get the atmospherics conditions to witness it.

I'm using this formula https://www.calctool.org/astrophysics/earth-curvature

There is no curvature to find.

FE Airline Pilot - yes, according to globers the peak would be impossible to find.