Klugeryid,
There are two broad schools of thought but there are many more subdivisions within those schools. What you are calling “Constructionist” is typically called “Originalist” when applied to the Constitution (as opposed to ordinary statutes). I am an Originalist. Which means that I interpret the Constitution as it would have been understood by an objective reader at the time it was ratified. (Note, however, that even Originalists will occasionally have to engage in Construction where they seek to apply the Constitution in area where it is vague or ambiguous.)
The other school, Living Constitutionalists, don’t maintain that they have a right just to read in whatever they want. Rather they believe that interpretation of the Constitution can and should change where the society as a whole has changed. But even living Constitutionalists would require evidence that societies mores have changed regarding the matter before them. It is possible to make the argument, that from a living Constitution perspective (assuming State Constitutions match this) impeachment requires a statutory violation. But this argument is not that strong because ultimately there is no check on the Impeachment power (other than voters). Therefore, whatever Congress and 2/3ds of the Senate say is impeachable becomes removable. Because practically it does not require a crime a Living Constitutionalist would not be inclined to read the requirement of a statutory crime into the text.