I'm not advocating theft or anything like that ... but you could perhaps "recycle" a Do Not Disturb sign from your favorite hotel. Heck, if you're a frequent guest, they might even give you one (albeit, with a rather bemused look) just for asking and explaining why you want it.

Alternatively, you could spend a few minutes on your favorite presentation or word-processing software and print a small sign to hang around your neck--for a few cents more, you could even laminate it and re-use it.

AA doesn't have to present you with every solution to your travel preferences--be creative.

cheers!