should buy the TSA padlocks. They are the only way you can 'legally' lock your checked luggage. Ive always found McCarran very helpful. I tell them whats in the checked luggage and then wait while they inspect it (if they wish to). Flying with AA they do this kerbside at the international terminal straight out of the back of the car if its not too busy. Then they seal my cases up with rolls of 'TSA security checked' tape. If anything has been opened or tampered with I could tell immediately. I usually travel home with 5 to 7 checked pieces and 2 carry on. Never had a problem yet.
Last visit I checked in at 7am before heading back into town and only left the Palms show an hour before my flight left.