Re: Stubborn green water in an in-ground pool.
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.
Re: In-Ground, DE Filter Pool With Clear Green Water
Just thinking. If budget is not a big problem AND you are not planning to re-plaster next spring (which would fix the stains), THEN you might want to do this:
1. Drain the pool.
2. Do a BLEACH rinse to remove as much algae as possible.
3. Refill with soft water.
4. Superchlorinate -- no stabilizer.
5. Then, transition to stain clean-up.
6. Then set up your pool for normal use, and a good winter shutdown, so you are ready to go next spring.