OK, British Airways Cargo here in Atlanta said that they will take care of us... that they can do this type of thing as long as they have a heads up to get the proper staffing in.
So, they will have someone there on Sunday, August 5th for us
Also, even though I offered to pay an extra fee they aren't charging me anything extra!
Woohoo! They are supposed to be sending me an email so I have proof they are ok with this in case the people we need to book the pets tickets with don't want to let us book due to the ATL/weekends thing.
Now just to figure out the timeline for that day.