IMHO the smart way to go about doing this is to make a TWRP or Nandroid backup of whatever you're running right now, pull a copy off the phone just in case, downgrade to the 4.1.1 stock TouchWiz ROM (the modem alone is enough if you're on TW 4.1.2+, in any case you might have to skip the bootloaders as those won't downgrade. Assuming you're flashing the "whole" ROM you must factory reset, hence the backups) do the unlock then restore the backup.
My phones: Galaxy Note II SGH-T889V (with LTE enabled
/ ext4 SD card support on TouchWiz ROMs
), Motorola XT-1045 Moto G LTE (TWRP
Previous phones: Nexus S GT-I9020A, Galaxy Gio GT-S5660M (Arpeggiomod ROM
/ Discussion, stock rooted ROM
), Motorola XT-1032 Moto G.
Phones for which I play "tech support" for family and friends: Galaxy Nexus GT-I9250, Galaxy Q SGH-T589R, Galaxy 551 GT-I5510M, LG C-800G Eclypse, Motorola XT-1032 Moto G