I think I followed protocol by getting pH to 7.5 and TA to 120 before measuring zero Total Chlorine (despite using 3" tabs in parallel with the filter). CYA tested at 100, but the water was too green for that test to be meaningful.
The dealer tested CYA at 54. I've removed the chlorinating tabs and have been diluting steadily. It should be below 50 by now.
Shocking to 20 and repeatedly raising it back up above that level cleared the green in a few days, and the filter removed green residue.
The water remained blue-green, and I could only see 3 - 4 feet down into it. It is not sufficiently cloudy to discern any color when removed from the pool and viewed through a clear glass.
Another week of keeping CYA above 17, brushing, and vacuuming produced no color change, no filter pressure change or residue, and no change in the rate of consumption of Chlorine.
So I shocked to 30. That level held overnight and declined only slightly the next day. (The pool is covered.)
Is this haze something non-organic? The pool has always been refilled from the house supply, which is well water run through a water conditioner. That was also the case before I bought the place and it had crystal clear water.