I would also say look in a junk yard for a tire carrier that is not going to need the key. Most use the 3/4" or 7/8" that the lug nuts use, so take along the tire wrench from the donor vehicle.
Some require you push in and turn to drop the tire, that is what is on my Bounder, a junkyard Ford tire carrier, I installed it. It cranks up into place, but I have to put in the crank, and push the crank forward while also unwinding it. I am glad to hear they have systems on the 2011 trucks that crank both directions, migth be worth it to change mine to a more modern style, that is easier to lift and get back down.
Fred.