In The Island of Doctor Moreau they chant: "are we not men". So my question is: when we place not before men, not after are, what we are implementing?
When not comes before men, it is merely being left in place.
In yes/no question formation, the verbs be, have, and the modal verbs are fronted (i.e. moved to the front of the sentence). If none of these verbs is the inflected verb, we get do-support, which works effectively the same way.
When the alternate form of not is used, namely the clitic/suffix n't, it does move to the front along with the verb, but this is because it is attached to the verb, so it must move along with it.
So, leaving the negation in place is the normal, default behavior for this kind of sentence, and a yes/no question where a free-standing not does move from its base position is the special case.