You need to start with your base Nebula comps. For example, go into "Nebula_2" and change the expression from time * 25 to time * 36. That comp is 10 seconds, long, so you need to start by having a full evolution loop of 0 - 360 degrees. An even better expression, though, is this time * (360 / thisComp.duration) which will work on any comp, regardless of the length (and as long as your Fractal Noise runs the length of the comp.
Next, twirl down the "Evolution Options" and enable "Cycle Evolution." Set the number of cycles to "1" and your 10 second comp should loop perfectly, even with the Turbulent Displace effect enabled.