Tips for packing electrical cables near Giant Quick-E bottom bracket I've been having major trouble getting all the cables back in after removing the bottom bracket electric motor from my Giant Quick-E. 

It's a rat's nest down there. There are cables coming from the seat-tube, cables coming from the downtube and cables coming from the Yamaha electrical motor, combined with many connectors. 

I physically don't have the space to tuck the cables away when reinstalling the electric motor. 

Does anyone have any tips? 

In the image, both red circles have to align. Perspective might be a little confusing, it is taken facing the bottom of the bottom bracket, with the drive motor pivoted out of the way on a single bolt, held in place by a strap. 

Regarding the tie wraps in the picture, the guys who assembled the bike at the Giant assembly line clearly also had issues getting the cables all in there, because they broke two connectors closing it up. Yes I could replace them, but the copper is intact.
Cable ties/zip ties can add bulk.  You might be able to recover some volume by changing them out for thin tie wire, looped exactly the same way.

Second thought - there's a lot of wire in there.  Can you shove any of it back into the tubes from which it comes?

Lastly, there are some black cables on the lower-left of your image.  Looks like they might tuck into a recess in the underside of the housing?    Try to methodically back-fill starting at the least accessible wiring, and then work outward covering your first efforts.    

TBH it looks like a difficult task, and I don't envy you.  Work with lots of illumination, and perhaps a selection of push-tools and pliers.  Take your time, and see what you can achieve.

And if it is just not going together, shake it harshly while pressing the cover closed, exactly like the factory did!