I had an algae once with one of my hydro girls. Same thing as you.. The rockwhool cube was green and the water was cloudy. But I am surprised that you have such a problem seeing how very little no light can get into your rez. I could be wrong here but algae doesn't grow in the dark.. The only thing I can suggest is taking those paper covers you have and replace them with something that doesn't transmit light. I also like the bleach idea but have never tried it. I cured mine by covering the rockwool and doing a series of washouts with hot water for the rez and lid only. I did that over the course of 4 days-everyday along with pure chilled water for the roots. It cleared up and plant is doing great.
Bust of luck!!
Sorry, read last post first. Reservior and bottom of trays were exposed. Covered everything now, flushed with algaecide, and H2O2. Think its solved.
Thanks