One clue was the official Vatican press release on the funeral that stated that the body would go through the Santa Marta Door. This door (under the Alexander VII monument) leads to the outside, so how did he get into the grottoes under the basilica.
Fr. Edward McNamara, LC recently reported that the body was taken through the Scavi entrance into the grottoes, therefore solving this minor mystery. If you ever get a chance to take the Scavi tour of the Necropolis, you'll be following the path of John Paul II.