I let the pool get icky and now I've got to clean it up. The short version is, if I shock the pool to 30 ppm will it burn off dead algae?

Here's the whole story (only the cleanup portion, not how it got this bad to begin with).

Started Monday evening with 10,000 gallons of stinky dark green slime with scum on the surface. Removed leaves from skimmers, ray-vac robot and surface, hosed off filter cartridges, added ~1.5qt. muriatic acid (pH was in the stratosphere) and 1 gallon of 10% sodium hypochlorite chlorinating liquid. CYA in my pool is currently negligible and this equates to about 10ppm in the absence of a huge demand, which I obviously had.

By Tuesday morning the situation had somewhat improved to 10 kgal of cloudy, avocado-colored water. pH still above 8 but I was out of acid, so I put in another gallon of sodium hypo (FC was 0) and went to work. Cartridge filter pressure was high, but I decided to hope that the chlorine would dissolve some of the algae and this would improve.

By Tuesday night I had very pale cloudy water. I added 3 cups of acid, which should have brought pH to 7.2 . FC was 0.4 ppm so I put in another gallon of sodium hypo. The cartridge pressure was still high, the cartridges are 4 years old and cleaning them doesn't help for very long any more, so I went ahead and ordered new ones.

Wednesday morning (today) the apperance of the water and filter pressure were unchanged. The new cartridges will be here in a few days. Hosing down the old cartridges is a fair amount of work and might not make much of a difference (hasn't been, lately). But I want to reduce strain on the pump motor and remove as much particulate matter as I can before installing the new cartridges so they don't get all clogged up immediately.

So... somewhere I thought I read that a 30 ppm concentration of Chlorine will burn through everything in its path. Could it help disintegrate some of the dead algae floating in my pool or is filtration my only hope?