I look at it as something akin to the John Crichton/Scorpius/Harvey situation from Farscape…
John has Wormhole knowledge in his head, implanted by the Ancients, Scorpy wants that knowledge so he can create Wormhole weapons and use it to destroy the Scarran Empire, so Scorpy implants a Bio-Neural chip that contains a mental clone of his personality into John’s head to extract the wormhole knowledge, Chip-Scorpy is supposed to stay hidden, but somehow, John’s subconscious is able to interact with him…
John eventually gets the chip removed, but an echo, an imprint of Chip-Scorpy remains in John’s head, John is more able to directly interact with this echo, a Neural Clone of Chip Scorpy, John dubs the clone “Harvey” (after the Invisible Rabbit of the same name)
Chip Scorpy was singleminded, occasionally possesing John, and preventing him from killing Scorpy, the NC started out this way, but through extended interaction with John, his memories, and his personality, Harvey developed his own personality, a strange mix of Scorpy’s scientific intelligence and John’s offbeat sense of humor, after a time, John began to, if not outright trust Harvey, to at least tolerate him, and to be fair, Harvey did work to save John’s life many times, sometimes even working against Scorpy
I see HeadSix as Balty’s version of Harvey, maybe Balty did have a neural chip in his brain, maybe he still does, maybe not, but HeadSix has more in common with him due to her interaction with Balty’s memories and experience than she does with any “hardware” based Six, HeadSix is a Neural Clone of Six