Wow, I did completely misunderstand what you were trying to do. ☺
If I’m getting it now you can achieve what you’re trying to do by using a variation of the trick GSG used in their card flip tutorial.
In this case you’re going to use a random effector get the start look you want, but you’re going to use a Shader Effector to animate the weight of the random effector.
Steps:
* set up random effector for desired position/rotation;
* in the random effector’s Falloff tab, set Weight to 0%;
* create shader effector, zero out parameter tab but set “Weight Transform” to 100%;
* add a noise shader in the shading channel;
* inside the noise shader, animate Brightness to randomly cancel the effect of the random shader.
Example: 12703_randomtestrandomtime.c4d.zip