Since you are a chemist you should apply your professional expertise to the interactions between chlorine and algae. The idea that chlorine won't kill algae no matter how high the level is simply untrue.

On a Saturday in the middle of May I opened my winter cover and found green slimey water. Algae. I filled the pool up with water from the hose, turned on the pump, then dumped 4 gallons of 12.5% liquid chlorine into my pool. That raised my FC to an estimated 24-25ppm. 24 hours later the water had gone from green to blue, though still cloudy with dead algae. That was less than a month ago.

I have added to my pool this spring:
Bleach/Liquid Chlorine
Dichlor
Trichlor
20 Mule Team Borax (2 boxes)
Arm&Hammer Washing Soda. (1 box)

My pool is clean, my water glistens.
My FC is about 5,
CC 0
TC 5
pH 7.6 (been there for weeks)
TA 60 (in theory too low but with rock-solid pH, I'm not messing with it.)
CYA 30
CH 60

I occasionally add CYA, dry acid OR Muriatic Acid, and PolyQuat.

That's all I use.

Carl