when semiconductor boules are czochralsky grown, afterwards impurities are swept away by heating a zone, and moving the heated zone (the impurities dissolve better in the hot solid compared to cold solid), could one similarily move the gold by such transport?

instead of a heating device, a large mirror could focus sunlight on the asteroid, so that one doesn't need to do induction joule heating powered with solar panels

I'm wondering if simpler solvents for gold (like mercury) could work

Or perhaps faradayic electrodeposition of iron? like how conducting current through 2 copper electrodes in a copper sulfate bath can transport copper from one electrode to the other.

Obviously any proposals would have to be tested on Earth before porting to space...

A lot of processes commonly used on earth are not necessarily the most efficient ones, certain aspects like environmental regulations or poisonous or dangerous-for-human substances can preclude their commercial utilization, but that doesn't mean an automated refinery in space should avoid it too. Thus we can't just point at the properties of on-earth-commercial methods and assume space-based refineries would have to inherit the same issues.