So, your suggestion is that we just remove the current Constitutional definition of "active" and then redefine it later in the statute?
My suggestion would be to strike the present definition of active and then say that the Senate shall have power to define what an active voter is by appropriate legislation. Then get the Senate to do it by appropriate legislation.
It should be noted that as a scholar of this sort of stuff I have a bias towards a constitutional structure that leaves as much to the legislature as possible. I'm a great believer that the constitution provides the skeleton of the law and the legislature provides the flesh of it. There are certainly viewpoints out there that disagree with my methods, so don't necessarily defer to me all the time (but certainly don't let me stop you!)