I am just going to go out on a limb on this, someone correct me if I am wrong.
One, your lighting time is prob too long. Try 8 or even 7 hours with a 2 hour break in between.
Two, get a gravel siphon and such that stuff up.
Three, you need more plants.
Four, I do not see why a blackout for 3 or 4 days would hurt anything in your tank. You need to clean out the majority of that first though.
Five, you need to know your water params. BGA is caused by poor water/tank management if I recall. I am battling a bout of what I think is BGA slime because my tank had to go three weeks without a real water change and my bioload is too big to do something like that. Get your water in check or it will just return.
Speaking of which, and not to thread hijack, but does BGA/slime (side note, it is not actually an algae) look more black on plants? I thought I had BBA but everyone elses BBA I see look hairy and mine is just a black slime coat on things.