Old thread, but figured I would weigh in on the moving of flat files specifically full-ish ones. First of all, I would NOT trust movers to move a flat file with any poster in it. But when I moved to OK from CA, I had a U-Haul trailer. I custom cut foam core "lids" for each drawer. After putting one of those on top, I then shoved pool noodles in there to keep everything tight and prevent sliding around. A couple of drawers were full enough that I used half pool noodles. I put one on each side edge front to back, 2 supporting between those running front to back, and one in the front runing side to side. I also ran shrink wrap around the whole thing to keep the drawers from trying to slide open. The whole setup cost me about $15 bucks and it worked perfectly. No sliding, no damage.
I actually still use the foam core lids to prevent any damage from opening/closing, and it especially helps for being able to store a rolled poster until it is sufficiently flattened.