Would it be possible to allow facegen manipulation for a mirelurk king?

No.

Only PlayerModels come with Morph-able Head-meshes.

The faces of the Mires are part of the model.

What if one was to chop up the mirelurk king mesh?

The only way you would be able to get morph-able creature Mirelurk king faces is if you were to morph them directly in a model editor. You'd might then want to set things up so that the creature had both a body piece and a head piece in order to use the changed faces (splitting the mesh into interchangeable pieces you see). Quite a lot of work on it's on accord.

You could actually get a facegen head out of the Mirelurk king's head for use with the player model however, but the process of creating it would be even more tedious and time consuming. You'd basically have to take the head and then create morphed variations of the head corresponding to all of the different vertex flexes for face movements. Once that's done, combine all the flexes into it's own file to work alongside the standard head mesh. As far as I know, only around three or so people to my knowledge have messed around with such work. And I learned about all this from throttlekitty.

What about the bermecian mod? I believe that does not use the human head mesh but you can alter it with facegen. Did they do what you mentioned above?

It actually does use the headhuman mesh, but it makes use of a race entry's face sliders plus custom textures to give the appearance of an animal-like face. I believe there was a fox race mod for Oblivion that did the same sort of thing too.