Here's how you can test: Set the sensitivity to 1.636364. This makes a 360 exactly 10000 counts. Now set the FOV to 1.55 (or 110 in-game).
According to your calculations this will make the actual HFOV in 16:9 124.59 degrees. According to the calculator it will be 123.27, so a difference of about 1.3 degrees.
Line up something like a pillar at the right edge of your monitor. There is a slight sway so preferable line it up so it barely touches and edge on the left end of the sway:
With your calculated FOV the distance in counts to the edge should be 10000/360*124.59/2=1730.4 counts, according to the calculator it should be 10000/360*123.27/2=1712.
So this is moving 1712 counts wich perfectly lines up:
This is 1730 counts which overshoots:
It more complicated than this though, because 360 calculations for ADS and scopes are seemingly a bit more accurate using the FOV from your approach, but the actual FOV seem to be off.
I need to do some more testing to see exactly what's going on here.