Even though direct copper poisoning is a possible idea, the amount of algae you are describing sounds a little much for that new of a tank, I'm wondering if items like pH shift greatly, really greatly, in between morning and night cycles thereby stressing them enough to die. I've really never seen a tank develop any green hair algae at all during a cycle aside from some simple brown diatoms on the glass. If it was a tiny bit of green algae on some rock or on a small part of the glass I'd still chalk that up to normal phases, but green infestation simply means you have something rotting in there during a clean-only phase and this is problematic. Imagine that algae getting a footing before any animals are even added, if we don't find your algae problem just as importantly as your invert problem you'll be robbing Peter to pay Paul and soon you'll dislike the tank due to constant algae battles.
I've had many aquariums and have never had that problem with algae, somehow during your cycling there were nutrient accumulations and sometimes these wastes, if considerable enough, can cause wild pH swings depending on how you manage your calcium and alkalinity. Either way I'd like to see a pH reading taken at 7 am and 7 pm for a 4 day cycle, to check the data for consistency. copper is a great first suspect just guessing, but I'd also look for nutrient loading and simple water fouling that may impact basic parameters and cause pH shock--just brainstorming.
I've also seen people use really dense/animal loaded live sand from established systems that took that system's aged detritus load and deposited it in a clean/new system they thought could keep all that life fed as it did in the aged sand...the giant aged system had nutrient cycles that fed a dense sandbed of dying and reproducing pods and worms galore, then when starved in a new tank these items died slowly altogether and were only algae and alkalinity suckers for the life of the new tank. I say start clean, add only a tiny bit of aged sand, and what thrives is in relation to the capabilities of the system.
Brandon