Remap time without affecting "Time Displacement"-Effect. Is this possible?

Hi everyone!

I'm kind of trying to combine two tutorials Aharon did a while back. I want to make an animation of a nice sinus shaped waveform, but still have it follow certain curves.

What I've come up with so far, is this:

I'm using AE 6.5 on an Intel MacBook Pro.
All comps are 4 secs at 25 fps


Comp 1:
Solid with a line-shape.
Line shape gets Stroked.
Stroke gets Wave Warped with the Wave Height being animated from 0 to 35 over 4 secs.
Wave width = 6.

Comp 2:
Solid with Fractal Noise.
Fractal Noise has complexity of 1, and is stretched vertically.
No animation yet, but I plan to animate the anchor-point horizontally.

Comp 3:
Contains both previous comps.
Comp 2 is hidden.
Comp 1 gets "Time Displacement" Effect with max 2 secs displacement. Displacement map is Comp 2.

When I look at the 2 second mark in Comp 3, the wave-shape looks great.
I'd like to freeze the instance of Comp 1 at the 2 second mark, so that it looks like this throughout the animation and I can have Comp 2 animate to change the shape.
But when I use Time-Remap, the trick doesn't work anymore, because to the Time Displacement effect the timeline looks all the same, too.

Does anyone know a way around this behavior, or a different way to get the animation I'm looking for?
Thanks in advance!

Yours,
Andra