I'm not sure what they charge, but if you are flying Delta, they have a cargo service called "Delta Dash", which lets you send a package by air cargo and they guarantee that it will go on the flight you specify. You can pick it up at their office at the Atlanta airport an hour after the plane lands. The air cargo gets treated a little better than the stuff the baggage handlers "inspect". I'd pack it inside something like the plastic tote boxes the FRC kit comes in. This option is probably more expensive than FedEx. Most other airlines have freight or cargo services, too.
If you want to ship FedEx, there is a FedEx Service Center in downtown Atlanta at 401 Windsor Street SW, ZipCode 30312. It's about 1.7 miles from the World Congress Center (5 minutes), and you can ship the package to "Hold At FedEx" and then pick it up there. There is no extra charge for this service if I remember correctly. They are open from 8:00 AM to 8:30 PM. If you need to be able to pick it up before or after these hours, there is a FedEx Kinkos on Peachtree Street that's a little farther away but is open 24 hours.
Or just take Mannie up on his offer to have all the Vex robots shipped to his house
He's a great guy and you will not have anything to worry about if you go with that option.
I used to be in the overnight shipping business... No matter how you ship it please put your information both on the outside and the inside, including a phone number that you can be reached at in Atlanta. It was amazing how many things would have the airbill fall off or get destroyed and had no other identification. They usually figure it out eventually, but if there is no other contact info it can take a couple of days.