Wow what a project. I would not have the energy or patience to move everything out of my house. The painting portion of your project could be done with little interruption just by shuffling items around and covering those items, it's the flooring that is the more involved part of your project. If you are doing the flooring yourself, I would try and pack the small items and put in the pod and leave the bigger items and move to one side of the room, then to the opposite while the flooring is laid. If you are hiring professionals to do the flooring, I would check with them to see if the above arrangement would be OK or not. Liquor boxes are strong and just the right size as suggested already, and I also agree with the suggestion of removing drawers and then moving the item they go in, makes for less repacking.
After all the hard work is done, just think of how great it will look when it's all done, new and fresh.
