Some other translation of akuppa-ceto-vimutti are: steadfast/unshakable deliverance/freedom/release of mind
i.e. asava free mind of arahant.
As I suggested on the first page, Bahiya story is essentially one of dispassion (viraga), leading to knowledge & vision of release (vimutti-nana-dassana). I'd say that is comparable to the above. Not sure exact relation between viraga and knowledge and vision, but they seem to be pretty catch all terms.
Here is another telling:
Discipline is for the sake of restraint, restraint for the sake of freedom from remorse, freedom from remorse for the sake of joy, joy for the sake of rapture, rapture for the sake of tranquility, tranquility for the sake of pleasure, pleasure for the sake of concentration, concentration for the sake of knowledge and vision of things as they have come to be, knowledge and vision of things as they have come to be for the sake of disenchantment, disenchantment for the sake of dispassion, dispassion for the sake of release, release for the sake of knowledge and vision of release, knowledge and vision of release for the sake of total unbinding through non-clinging. — Pv.XII.2
I don't think Theravadins care much for talk of higher level teachings, as other sects might of secret teachigns and such. As others have said, better to talk about what teaching is appropriate to the individual. There is a graudal path, and for whatever reason (wisdom), some skip steps or go though them quickly.