You should be able to solve your problem by adding 7 gallons of 8.25% bleach at a time, and checking your chlorine level 3x / day. Your goal should be a chlorine level of 20ppm and each gallon of 8.25% should add about 2.84ppm of chlorine.

If you use 12% liquid chlorine, it will add about 4.1ppm per gallon and you'll need 5 of them to shock your pool (that's one full 5 gallon carboy).

40 gallons sounds like a lot, but if you didn't add it in large enough increments, your algae would just keep coming back. Since MY liner is old and faded, I'm willing to get my chlorine levels quite a bit higher to slam that algae to death.