Seems very curious. Small box, yet smoothing mains at 10amps normally needs a large capacitor, much bigger than your box.
What is the load? Is it resistive, or a coil, which could be "self smoothing".
Is the transformer centre tapped, for disconnecting half of a bridge rectifier setup doesn't by my reckoning halve the voltage. Sounds like a couple of thyristors, with a capacitor which charges up after a few seconds and then cuts to half-wave, using a transformer with centre tap 55-0-55. I am most intrigued. You may have to cut or dissolve away the potting on the box. Methylene Chloride = Nitromors Original is not nice, but ok if you use gloves and have some ventilation. I agree with Nigel Goodwin, more details please, as he is obviously thinking of a change from full wave to half wave rectification, (or even switched mode). Bill