I get your points, but remember that in FWWM the LMFAP puts his hand on Mike's shoulder and they both start to speak the same words at the same time. To me, that makes it very obvious that the LMFAP is the arm of Mike.
Well, if he's the arm of everyone, he certainly is the arm of Mike also.
Mike got rid of his arm, the body part that he used to act out his temptations and the will to kill. If Bob would be the evil that men do, or the evil thoughts and temptations of man and LMFAP would be the arm that people use to make the thoughts and temptations into action, Mike could represent a human being who's separated himself from the will to do evil. Then when facing Bob, Mike has to become what he once was to have the power to make Bob to give the garmonbozia away. Hence the contact between LMFAP and Mike. After all, that scene happens in a place where it's "natural" to show abstractions happening "in materials and combinations of atoms" (as Mrs. Tremond/Chalfont said in the script of FWWM).
Of course, it could be so that the abstraction as a form of a little man has been, mythologically speaking, created from this one man, Mike, getting his "evil" arm severed. But even so, the LMFAP could represent the arms in general. Just like BOB can be thought as being "the evil that men do" in general.