I had the same black growth in my tank the first time I looked. I tried weak bleach solution, vinegar, power washer, all with inadequate results. Someone suggested that the growth is probably a bacteria of some kind, as algae requires sunlight. I don't know if that's true, but I finally got rid of it with a very strong bleach solution of 6 gallons in a tank full to the brim. I let it sit overnight and voila, all growth dead and debris lying in bottom of tank. I pumped it out with a sump pump, got the last bit out with my shop vac, then filled about 1/4 full before pumping through the fresh water system. Two more rinses with dock water, then filled with dock water run through two charcoal filters, and flushed all the fresh water lines with that dechlorinated water.
I shock the tank once a year with 3 gallons of bleach, let sit overnight, and rinse/refill as above. The tank has stayed mostly free of growth on less it sits half empty for a few months. I try to leave the tank pretty full most if the time, and avoid using dock water if I can.
I also run the tank water through a charcoal filter before it is distributed to the faucets, shower, and the watermaker.
A small amount of brown stain remains in a few places on the sides of the tank, nothing I've tried gets it out.
Kent & Iris