Funnily enough, even as I talked to them on the phone, and was told that most likely 20th was accurate, I got an email about 6 hours later saying it was shipped and being delivered today (which it now has been). Good times!
Yeah... the rep I spoke to told me that if the scan isn't done at just the right time, it throws it into the next batch queue in the system, even though it's actually already been assigned a tracking number.
Very inefficient communications, but fast delivery!