Axelbacks don't increase HP, they are only there for sound. As far as the warranty is concerned, you really cannot do much to the engine to increase the HP without voiding the warranty anymore.
However, some people have installed a CAI (pretty much any CAI but Steeda will work) without a tune and I would say this would be your best bet, as you can install the stock one in about 15 minutes if you have to take your car in.
Also, using premium will gain you about 3ish HP at the peak of the power band if you are really desperate.
Some dealerships go crazy, and will let you mod your car (by letting them do the work) and still upholding the warranty. This is only very select Ford dealerships though, depending on the business owner.
2012 Black 3.7L =Performance Package