Look around in the pool stores nearby, and see if you can find any products by United Chemical, like "Yellow Treat" or "No-Mor Problems". These contain sodium bromide. Chlorine converts bromide to bromine, which is NOT affected by stabilizer. Adding bromide to a high chlorine, very high stabilizer pool like yours results in a small FREE and UNstabilized bromine residual.

There's a down side to this, explained here: once-a-bromine-pool-always-a-bromine-pool.html. But, since you may have to drain your pool anyhow, that's not such a big deal.

Anyhow, see if you can find some bromide based product. If you can, add 1/2 the recommended dose -- you can always add more, but you can't take it away. And, with 1/2 dose, you may not have high chlorine loss after the algae is gone. But, since the alternative is to drain and refill, so you can lower your CYA, there's really not much risk anyhow. If you get too much bromine in the pool, you just have to do what you'd have to do already, because of the super high CYA.

The other alternative is to take your chlorine up to 50+! This 'breaks' your pH test, and means you may have VERY high chlorine levels for a VERY long time after the algae is gone.

I'd start with the 1/2 dose of bromide.

Also, if you can, take the Nature2 out, and simply replace it with pipe.

Other points:
+ copper doesn't usually lead to green water, ESPECIALLY when the chlorine and pH are high!
+ high pH in your fill water doesn't necessarily mean high pH in the pool. Check the fill water's alkalinity: if that's high -- regardless of pH -- your pool's pH will tend to be high.