The first thing I would do is create multiple layers for each scene instead of all of the art on one canvas. I would also break the song up into phrases that were no longer than 4 bars so you'll end up with a bunch of comps. Trying to do a three and a half minute song in a single comp is not going to be efficient, especially when the client wants you to change something in the second measure of the first chorus.
I have done a lot of this kind of stuff. One of my last projects like this was just over 4 minutes long, the longest comp was about 6 seconds, and there were separate layered AI files with all of the graphics in their hero positions on separate layers for each phrase I would be animating. Most comps had less than 10 text layers with text animators, a background, and one or two animated graphics that look similar to your designs. Keeping it simple allowed me to deliver the rough cut less than a day after the artwork was approved, make about a dozen client-requested changes to art, timing, and colors, and deliver 2 versions of the piece in less than 3 days. Most of my AI comps were exactly 4K frame size, and if I remember right two of them were 2X 4K wide (7680 X 2160) because I had a long wiggly line that needed to move across the screen. Animation presets that I have used on lots of other projects were used to animate the position of the layers so all I had to do was open up an AI file as a composition retaining layer size, drop in the audio for that comp, set the in and out points for the layers and add text if needed, then apply the animation presets and render the comp.
When all of the comps were rendered I just selected all of them in the Project Panel and selected Create Composition from Selected and choose sequence layers. The first test was ready for the client. When we had the final changes done, all of the comps were rendered and a Premiere Pro project was created so we could finalize the timing of the transitions between phrases, fine-tune sound effects, and make sure that all 4 of the different sound mixes were perfect.
I hope this helps. After you have done a few projects like this you will be able to visualize the way the artwork needs be laid out more efficiently and turn out some really good and creative projects on time and under budget, and that's always good.
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