How to operate transformers at lower voltage than nominal
Operating a transformer at a lower voltage than rated is just fine. As it's voltage that determines the field in the core (for an ordinary AC power transformer, things are calculated differently for a flyback), you're running further below saturation, so have lower core losses.

Unfortunately the same limitations apply to current as for running at the full voltage, it's the temperature rise of the windings. As you've less core heating, you can probably get away with a little extra current for the same overall transformer heating.

Lower voltage and same current means lower power throughput. Although core losses have fallen, the copper losses will be the same, so the overall efficiency is probably worse (for a 'normal' power transformer, MOTs with their huge fields are probably more efficient running at half rated voltage).