Let's do the numbers on the 275 miles photograph.

Here are the details regarding that picture ...
https://beyondrange.wordpress.com/2016/08/03/pic-de-finestrelles-pic-gaspard-ecrins-443-km/He was 443 kilometers away at an altitude of 2,820 meters, or about 9,250 feet.
This would result in 16,529.5 feet of the target object hidden behind the earth's "curvature".
Now, here's the actual picture (with the peaks labeled):

Pic Gaspard is the peak that's at 443 kilometers away, but the peak elevation of Pic Gaspard is 12,740 feet. So the highest point of Pic Gaspard should be hidden by about 4,000 feet of curvature, so nearly a mile of curvature, so about 3.5 Empire State buildings stacked up. But you can see a significant portion of Pic Gaspard, so there are parts there that should be hidden by close to 10,000 feet of curvature.
Grand Ferrand, at about 392 kilometers away, should be hidden by 10,547 feet (using the same earth curve calculator), but the elevaton of Grand Ferrand is only 9,049 feet. So Grand Ferrand should be completely hidden by about 1,500 feet, but as you can see here (compared to the silhouette above), it's almost entirely visible ...

On the 275 mile range picture, you can even see that smaller outcropping at the right, near that curved edge on the right (also visible in the picture) which is less than half the altitude of the peak of Grand Ferrand, so no more than about 4,000 feet in altitude.
Those visible features of Grand Ferrand should be hidden by 6,500 feet of globe curvature, or 1.23 miles, AT LEAST, since that would be if you could just barely see the top, and you can see nearly all of that object to the right and the bottom of the curve.