After Effects - Unknown Exception error while working with ai files

The first problem I see is that you are editing a movie in After Effects. The "Davidson" comp is full of nested comps. All but the last nested comp would preview in real-time on my system, but a more sensible workflow would be to render all of the nested comps to a production format movie and then do your editing in Premiere Pro, where you have a much more efficient way of timing the cuts, adding music, and doing final color grading. That is how a major studio would handle a long-form project. There is too much risk of the final render failing as it churns through all those nested comps. You won't save any render time in the long run.

Layer 6, the "57 & 58" comp, was the only part of the main comp that seemed to have a little problem with the preview, but once everything was cached, the 1/3 resolution preview ran just fine.  Switching the Comp resolution to Auto gave me a Full resolution preview that took about 4 minutes to cache but then played back just fine. 

I suspect that you are just running out of system resources. 

I looked at a lot of the supplied AI files, and there did not seem to be any consistency in the layout or artboard size. I would have been a lot more careful with the artboard sizes and made sure that everything was set to snap to pixel and the artwork was in or at least close to the hero position on comp-sized artboards. That would speed up your workflow. 

I did not get any errors, and I tried importing many of your AI files as compositions. None of them gave may any problems other than the odd frame size of some of the artboards. 

Sorry, I could not be of more help. I could not find any problems with the source files that gave me any problems. Keeping each comp to a single shot and rendering them before trying to edit the final movie will make your life easier, and it may solve your error message problems.