Halo Flare Jumps in Animation

Included vids of the problem I wish to solve below with a blend file for the diagonal example.

halo_flare_jump.blend (536 KB)

Trying to figure out a way around this jump that occurs when the flare crosses the middle of the camera frame. I assume that the reason why it jumps is because of the 2D nature of a halo material, and I am hoping that there is a hack to fix this, as I have been unable to find a solution on the internet so far.

Thanks in advance for the help.

Here is another example, this time I animated the camera moving instead of the object that represents the origin of the flare.