when firing a projectile north
the Coriolis effect exists because the speed of the surface of the earth changes based on it's latitude causing the projectile to be moving faster sideways than the earth at that location.
the projectile simply moves in a straight vector and the earth moves underneath of it.
however this projectile has to fight against "wind" that behaves as if the projectile is slowly changing direction and will slow it down somewhat.
It is also worth considering that this sideways motion will be slowly converted into "vertical" motion because the sideways motion is tangential to the earth.

I am assuming that the atmosphere moves with the earth

Does that sound right to you or am I fucking crazy?