I see that a lot of folks built their 4pis and attached the back as the last piece. I thought about that, but then I couldn't figure out how to get the cross bracing installed, so I decided to leave the top for the last piece to glue on.
I had some leftover 1x2 maple from a cabinet I installed, and decided to use that. The plans say to install the cross braces with a "slight amount of preload". I took that to mean that they should fit really tight, so I cut the braces 1/16"-1/32" too long, and really wedged them in there. They weren't going to move easily, but I glued them in to be safe.