The first thing that stands out in the file is that it uses Instances instead of Multi Instances. As mentioned above, the use of Instances allows for time-based individual clones. However, the render time will be multiple times higher with instances.
The key question is, since you do not move the camera at all, why the trees farther away from the camera need to be in 3d? It could be an image sequence instead. It would require a lot of pre-rendering and organization, as the light direction, as well as the random rotation of the trees, needs to be addressed. So that is not practical. I tried it this morning.
The option that I presented with child-object-sequence can have that twig movement. So the Modify Clone parameter is used 0-90 % for the grow, and then 91-100% is used for the motion, which means it goes up to 100 then down to 91% again and cycles from there. This would be the way I would suggest it.
Why everything is black in the frame is not clear to me, since I do not have any data from the render-farm. I have only a limited system here, considering your set up, and it runs out of memory (32GB) quickly with your scene, so I have to reduce the clones already to get anything done. The Render Settings> Options >Ray Depth was set to 6 in the provided file, which is certainly way too low.
However, at least the trees close to the camera should have shown some texture, as the first six layers would be fine. That might be half a tree or so. That everything is black, might indicate that not all data was available.
I have had switched the FFD off as it looked not OK. The trunk moves up and down. You can fix that with a Restriction Tag and a Selection. So the trunk stays on the floor.
The Time Track is working. However, as your project time advances, the effect of the Time Track advances as well. The offset in Plain Effector is given as a constant. Then the Falloff takes that offset away and shows the animation. See example:
I consider the time 96 to 192 as the main time for the project.
You might want to set the offset to 196 frames. The effect will be similar but sharper. At the moment, the time moves forward, the animation changes, and the effect of the Plain Effector, while the time moves back to “normal” will be stronger. Set the offset to 48, and it might become clear.
I will try differently. The Offset change, the project time, as well as the animation time of the PLA itself, are a combination. The further the time-slider moves, the faster the effect of the Falloff to eliminate the offset.
I stick with the Multiple Child sequence suggestion as to the workable way while using the 0-90 forward; 91 to 100cycle idea.
All the best