Like Rob said, ship your ammo.
Here is how it works in the God forsaken nations capital @Dulles:
Arrive with case and locks in place. DO NOT USE TSA LOCKS. Go to check in counter. The attendants are not idiots, not even here in liberal land, and they will immediately ask if you have a firearm. When you tell them yes, they will have you sign a form certifying that your weapon is unloaded which will be placed inside the case, I just remove the bolt and have it in the case separately. The airline agent will then accompany you and your rifle to the TSA baggage scan point. Once there you will give them the key to your NON TSA locks, and they will open the case, look at the weapon to see that it is indeed unloaded, lock the case and hand you back your key. You should be the ONLY person with a key to be able to open that case.
I applaud the TSA and airlines if they now require you to pick up your rifle at the counter at your destination. I returned to Dulles once and waited about 1/2 hour after my baggage came out for my rifle. Since it was an oversized item, it came out at a different point WAY the hell away from where I was with no one standing by to keep watch or to see that I was the owner of the case. Anyone could have picked it up and rolled out! And it ain't like no one knows what the hell is inside a Pelican rifle case with Nightforce / BCM / Armageddon Gear / stickers all over it.
All in all, it's amazingly simple. And I think it goes without saying, DO NOT open the freakin case anywhere in the airport other than for TSA, or you may be snackin on dirt, face down, with a dog biting you on the ass!
Good Luck In The Match!!