@Jacob — Thanks for the link! It’s very useful.
Using an Optics Compensation effect (reversing the lens distortion and stretching the field of view) coupled with a small amount of Fast Box Blur is getting me very close to what I’m looking for in terms of the softness.
I may have to mess with Particular a bit to get the shape of the streaks more in line with what I want. The light rays in that original video have a nice taper to them on both ends, whereas mine are straight rays. That tapering adds to the sense of the beams streaking by.