The quickest and easiest way to get both chlorine and CYA into the pool is to use Dichlor powder. Just keep in mind that for every 1.0 ppm FC that is added, you will be adding 0.9 ppm CYA. So adding enough Dichlor to get to around 20 ppm CYA should be enough to prevent the huge reduction from sunlight while not being too much until this algae problem gets cleared up. Once the equivalent of around 20 ppm FC or CYA is added via Dichlor, switch to bleach only at shock levels to get rid of the algae.

I just figure using only bleach at this point is going to be hard since it will be burning off very quickly from sunlight in addition to getting consumed by fighting the algae. I agree that you need to be careful to not add too much, but that can all be calculated readily based on what I said above (i.e. don't add more than 20 ppm FC worth of Dichlor to the pool). It takes 3 pounds of Dichlor per 10,000 gallons of pool water to raise the FC by 20 ppm and the CYA by 18 ppm.

Richard