I just used a relocube this past Tuesday to move from Atlanta (Sandy Springs) to Austin. My window was 8-12 p.m. I was hoping they would arrive earlier, but figured I should plan for the worst case scenario. I scheduled the loaders to arrive at 12. In speaking with them, they knew my situation (I was leaving town immediately after the relocube was loaded and my condo vacuumed) and were willing to be flexible and arrive within an hour of me calling to let them know the relocube had arrived.
As it turned out, ABF didn't get there until 11:35 and by the time they unloaded it the loaders showed up. I was soooo glad I hired professionals because there is NO WAY I could've gotten all of my stuff in there. Be forewarned... the relocubes are MUCH smaller in person than they look online. Let me know if you'd like the contact info for the loading service I used.
Good luck with the move! I'm in Austin now but still recovering.