I wouldn't worry about what order your barrels fill and drain in... I gave up on my system. Even with fiddling every day for a week, I couldn't get my system to be consistent. Some of my GBs fill in 8 minutes, some in 15... I just try to adjust what grows in each bed - stuff that doesn't like being wet goes in the beds that take longer to fill.
If you can figure out how to post pics of your system, it might help.