Ok, so here are the latest measurements using the pool store computer: (my Taylor kit is still being pondered by Amazon)

FC: 3.15 (notice the drop from 16+ from the last time)
CC: 0.59
TC: 3.74
PH: 7.7
Hardness: 27 ppm
ALK: 119 ppm
CYA: 12 ppm
Copper - 0
Iron - 0.4 ppm

The guy explained that when total and free chlor are close, it leads to murky water.
They also suggested adding 65 pounds of 'Calcium Hardness Control' to bring that up.

Then, a bottle of Metal Away followed by 8 capfuls of Alum (some sort of sequestering agent) to the skimmer and let it run for 48 hours, then backwash and repeat.

Just for fun, I put in a few Ascorbic acid tabs in a calm section to observe any change to the liner - nothing.

The murk seems a bit better today, so perhaps it is just a matter of continued filtering? The liner verticals look good (blue).
Edit: adding in a bit of DE as well. Shame it only comes in 25lb boxes.

Is the Pink Stuff similar to the Alum? Between the shipping cost and delay, I'd hate to have to go that route (nobody sells it locally).