Fortunately I just sent a rotobrush shot to the renderer so I have time to dig into this problem.
I see a couple of workflow issues. First, it's possible to put multiple beam effects on a single layer. Just duplicate the first beam effect and select composite on original. I would do that or pre-compose all of your beam effects if you want to effect all of the beams at the same time. You can also apply displacement map to the bottom of the beam stack like this:
Second issue, if you have gray over beam 1 and black over beam 2 and white over beam 3 and a different gray over beam 4 then the end points are going to move in different ways. If you want the end points to stay fixed then you need to do an overlay on the end of the beams so the end points all stay in the same position. A luminance value of middle gray will keep the ends in their original position. You can do this with a gradient shape layer, a gray solid and your fraction noise layer and a blend mode in your pre-composed displacement map. (what I would name the comp with the fractal noise).
Here's another thought. The displacement is going to look different on the lines slanted to the right vs the lines slanted to the left. Here's why. With a positive value for horizontal displacement black will move pixels to the left and white to the right. This will give the displacement a different look depending on the angle of the line:
To fix this problem you'll need to separate the left leaning lines from the right leaning lines and apply a displacement map with different values to the each pair of lines, one with positive values the other with negative values. This is not a bug, it's just math. I hope this makes sense.
I'm wondering why you have cameras and lights in the comp with the tracks. I'm assuming from your main comp screenshot that the footage is on the bottom and only the tracks are on the top. I also do not see any 3D layers other than the null and there is no camera in your Main comp so the camera is doing nothing to the layers in the screenshots. The only thing I would have in the beams comp is the beams and the displacement map.
If these workflow suggestions don't solve the problem we need more workflow details.
Thank you for your response, I haven't been able to get back to this project but will definitely try this method as well. I saw your comment on another duplicate thread and I apologize, I was either having issues with my internet or the website was having issues and it resulted in multiple duplicate threads.