Can a transformer output current be controlled by a current limiting switch on the input?
max current can be varied by putting variable resistance in series. 

this could be a carbon pile rheostat,a  variable inductor, magnetic amplifier, or even  home-made deathdrap like a scariac. a reverse wired variac driving a resistive load.

Another approach would be to use a motor-generator and to vary the generators field current to vary the output current.