Sorry to say but you still have to pay by credit card (huge trail), and even if you use bitcoin, you still have to have the phone delivered somewhere, and to someone.
One of the things to keep in mind, however, is that even if you order this phone and use it, it's highly unlikely that any organization will be able to track your phone within a 30 day period -- and even if they do, and they realize the phone is a BurnerPhone (unlikely), if they come talk to us we have no records of which phone was sent where, or even where things are shipped.
They'd have to query the USPS, and then they'd have to speculate as to which phone went to the person in question.