Fixing the "HasForeignDsk[s]" error on Seagate BlackArmors

My Seagate BlackArmor 440 NAS decided to restart in the middle of a write operation the other day, corrupting its RAID 5 volume. I managed to recover the data on the drives using another computer, but to my horror found that the NAS would no longer accept any of its drives to make a new volume with, displaying the titular error. After a few day's worth of fruitless Googling, I stumbled upon the solution.