Well, there are a few things here for starters. First, you can ignore the LED's as the cause of the issue. They do not phase shift like old T5 or MH bulbs do. You're currently testing positive for nitrites which means you also likely have nitrates bound up in the algae.
With all that frozen that you are feeding, I'm sure you've got phosphates as well. Phosphates and nitrates feed algae like nobody's business. If I understood your post correctly, you're feeding three cubes a DAY to your tank. If that is the case, you're putting a lot of nutrients into your tank. I have a similarly stocked 180, and I feed a half cube or so every day, sometimes every other day. All my fish are fat and happy, I suspect you could cut your feeding back quite a bit without issue. If you feel that you need to feed this much, you're going to need more nutrient export, either in cauleropa/chaeto or larger, more frequent water changes
Also, you had sand and are moving to crushed coral? This is a bad idea. Crushed coral is notorious for collecting crap and letting it decompose in your tank, which leads to more nitrates. You're best bet is aragonite sand, and adjusting the flow accordingly so that its not blowing around. I have oolithic sand (the smallest you can get) in a tank with ~50x turnover and I don't have a sandstorm.