Actually, I have no certain idea how FoV works in Minecraft. But I if we assume, that it works like an optical camera, I may help you.
Here you can see how world is projected to the screen (or matrix in camera).
So, to negate FoV deformations you should (using spherical trigonometry) calculate angle distance to center of the screen and take a tangent of it - now you have pure coordinate - distance to target in radius of some sphere. To find a pure coordinate of screen border, you may take tan(FoV/2). Then using screen resolution calculate distance in pixels on screen between center and target. Then again using spherical trigonometry calculate angle between Center-Target and, for example, horizon line, understand that it is unchanged after projection, and get your result vector by this angle and that distance.
But please,
don't do that!
I'm sure, more forge-like way exists to do what you want.
For example, this:
or net.minecraftforge.client.event.RenderWorldLastEvent.