Chlorine is Bleach. Bleach is Chlorine. Bleach typically comes in 6% and 10%. Liquid Chlorine typically comes in 10% and 12.5%. It is the brush that breaks the biofilm, chlorine that kills it.
If you use 10:1 Water:Bleach and give it a good scrub, you should be fine.
You might drill some holes in the ladder to allow more water to circulate. Do it carefully to not weaken the ladder.
Maintain your FC at the top of the recommended range for your FC. You should be in range, WHEN YOU TEST. If that means you need to dose above range so that you are in-range when you test, you should be golden. Range found here: Link-->
FC/CYA Levels
This whole situation happened because your FC got too low for your CYA, and you did not have enough HOCl to sanitize the pool, and algae took over.
You asked about the science behind the biofilm. If you want the science behind FC, CYA, and pool sanitization, here you go. Link-->
Pool Water Chemistry