DT, no, the results are additive - we used 1.14 for nautical miles so:
1.14*sqrt Ha + 1.14*sqrt Ho would for 37k and 250 feet give 219 + 18 = 237 nm.
Now there is a phenomenon of analogous propagation where the light waves are bent by atmospheric ducting. However at night I believe such ducting is unlikely. One would conclude that an observer at 370 miles (nm or statute) would be unsighted. Now if that distance was kilometres
The supposed "burning plane" would still not appear at "high altitude."
Why does everyone miss that part of his email? Even if he could see that far - the object would appear on the horizon! It would not appear to be a "high altitude!!!!"