Given your source water, I'd DEFINITELY recommend looking at the cost of a partial drain and refill. You actually don't want to drain ALL the way, since with a concrete pool you actually DO have to do all that "water balancing" stuff we normally tell people to ignore -- you NEED more calcium in the water than your fill water has.
Or not -- it would be easier to remover the stains with the soft water, then adjust the 'balance' later, after the metal is gone.
By the way, lime stone (calcium carbonate from the marble dust in plaster, probably) does NOT dissolve into pool water UNLESS your pH is low, as in below 7.0. Given your fill water I'd guess you either had (a) a period where the pH was way too low, OR (b) used calcium hypochlorite shock or chlorine powder for an extended period.
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