Took a look at your doubler, but it will not do what you expect. It can’t add a 5th station to a 4 station controller, rather it can add an addition station to a wire bundle that would otherwise be a wire short.
Primary use of such a system is a repair of a broken wire, so that a one wire (+ common) can perform a function of two.
The idea of such system is not new, and does not have to be limited to two zones. Rains bird, if I’m not mistaken, makes two wire based systems which can handle hundreds of zones using this technology.