Weird 3 Way switch wiring
What you just described in paragraph 3 is a bog-standard 3-way switch loop of the type used before 2011 (no neutral offered).  

Power is delivered to the lamp proper; the 14/2 cable brings down always-hot (white due to a Code exception) and switched-hot (black).  That is all that is required on a switch loop for a simple switch.  

A nest of 3/4-way switches acts like a single switch.  This 3-way complex is installed like a "switch loop".   Neutral is not present, ergo these (and most) smart switches cannot work here.  

You have two options: 


Run a replacement 14/3 cable from the lamp to Switch A, providing always-hot (black), switched-hot (red) and neutral (white).  Now the master switch can go in the switch A location.  In the old, inter-switch 14/3 you re-task red and white to be comms and neutral, respectively; black is capped off. 
Go with a different smart-switch line where it uses a module inside the lamp dome, which talks to smart-switch remotes in the current switch locations.  Then, reallocate the wires in the existing 14/2 and 14/3 to be actual always-hot (black) and neutral (white), to power the smart switch remotes.