Chlorine bleach is perfectly OK to use as an algaecide. The concentration needed to kill algae is well below the concentration needed to damage any paint I have ever heard of. But the concentration needed to eliminate your already heavy growth should be to just pour in a gallon and mix it around. Then you should reach in with a long handled brush and scrub it all off. Then wash out the tank. Or you can just use a pressure washer to clean it all off. Then after you have it all clean put in fresh water with bleach to make sure that all the residual algae cells are dead. Wash it out again and refill with fresh water and a little bleach to keep any re growth at bay.
You could also use alcohol, just like in windshield washer fluid. It is stored in a plastic bottle in a nice warn area and i have seldom seen a gummed up bottle. Unless the car's owner used plain old water.
For bleach you should be fine with a tablespoon in a gallon. And you can use as much alcohol as you want. Have you ever seen washer fluid damage the paint? Even up north where the alcohol is used as a washer container anti freeze?
