We need to adhere to the AEA. The very purpose and legislative intent of the Alien Enemies Act vests the President with extraordinary power, including unobstructed discretionary deportation power, to deal with and remove aliens from on American soil who may pose a threat to the general welfare of the United States and her citizens.
As to any "process" which may be due to those scheduled for deportation under the AEA, it obviously is a writ of habeas corpus limited to the narrow question of the detainee proving they are a citizen of the United States, and not an alien. Keep in mind this writ of habeas corpus proceeding takes all of a few minutes for the detainee to prove whether or not they are a citizen of the United States.