I'll try again. Moving the C.G. toward the elevator produces tail heavy behavior only when the elevator is toward the tail of the airplane. It's just that simple. Moving the C.G. toward the elevator on a canard produces nose heavy behavior because the elevator is toward the nose. In all planes, moving the C.G. toward the nose produces more nose heavy behavior and moving the C.G toward the tail produces more tail heavy behavior. The location of the elevator is irrelevant to this.

Your logic lead to the contradictory result that moving The C.G. toward the nose of a canard would cause it to behave as if it were tail heavy. The error in your logic is of thinking that the specific case of conventional designs applies to all cases of various airplane designs. This is an error of inductive reasoning. An example of the error is this argument. Bill is tall. Bill is a person, therefore all people are tall. Your reasoning follows that same form. In the same way it does not follow that because Bill is a tall person that all people are tall, it does not follow that moving the C.G. toward the elevator on a conventional design has the same effect on all designs. Any clearer for you?