It's finally finished. I spent most of my time watching frames render, then going back and finding tiny little errors, adjusting and re-rendering. All together, with all the layers, the animation had a total of over 11,000 separate frames. One of the other animators there helped me composite it together while I was render-wrangling. We finished it off, sent it out and got initial approval. The clients still have to pass it by their execs, and if they approve, it's all finished.
Here's some screenshots of the final version. For copyright reasons I can't post the actual video, but if I get permission I can probably show it in person.