Perhaps the reason that Bern isn't among the options overtly discussed is that this has been - as others have pointed out - a test to see if they can crack Maytag's biggest weakness. Granted, her feelings/commitment to Bern kinda counts as one but it seems like they really want her to be unfaithful. To have May break her resolve to be monogamous even in the face of her deep set desire to be otherwise. In that case pretending to be Bern wouldn't really accomplish that goal.
That's how I see it as well, it's some kind of challenge. Eager awaiting what the motives for all that are (aside from the sex-wanting) and also if the shape shifter is one of the female twins...
And it's her weakness (as pointed out by Moss) that they seem intent on testing.
I'm thinking that all these people with Danzig are "cursed" much like Moss. Escher, Fata Morgana, The Twins heck, maybe even the dog, Maximillian.
I'm betting thats why Fata's bottom half isn't showing. Maybe she doesn't even have a true form, or her abilities stem from a curse which causes her other problems. The interesting thing about her illusions seems to be that they are more real or solid. Heck if mental state is her speciality then maybe she just messes with people's perceptions.
P.S. anyone else note that although the apparently aren't nice enought to put them in the nice rooms instead of the dungeon?