Your conception about what is happening to the output from the cartridge when interfaced with a balanced input is flawed, insofar as you see it to be a negative. The signal is not "cut in half" per se, and there is no conversion of the signal from "two wires" to "three wires". The ground in a balanced input is independent of the + and - inputs. The cartridge sees only the + and - inputs and does not know the difference between +/- vs hot/ground in an SE input. One could make an argument that the output of a cartridge is inherently balanced in the first place; the choice of hot and ground is arbitrary, really.
However, your impression that your BAT phono sounds best with an SE input is not one I would challenge, since I don't know the particulars of that unit and you are entitled to your opinion. You might discuss your finding with BAT, however. Nor is it my intention to argue that all truly balanced circuits are better than all SE circuits, not by a long shot.
However, your impression that your BAT phono sounds best with an SE input is not one I would challenge, since I don't know the particulars of that unit and you are entitled to your opinion. You might discuss your finding with BAT, however. Nor is it my intention to argue that all truly balanced circuits are better than all SE circuits, not by a long shot.