As with most all other planted tank Q&A, it's about balance of nutrient and environmental ratios.
In my experiences, doing a 7 day blackout is about the only way to kill off a severe algal outbreak, and yes, all of your high light plants die... some or most of the mediums do too. Then when the lights come back, there aren't enough plants left alive to out-compete algal growth and it comes right back. Why? because the problem is often nutrient or co2 deficiency of some type.
Try simply reducing the photoperiod by an hour or two each day, and avoid over feeding. I'd mechanically remove what is easy to get to once a week or so. Do more water changes (around 60% - twice a week is what I usually do), and give it a month or two. If the problem gets continually worse then you could have a severe imbalance of nutrient that may not fix itself. For example, you may have to test your water for phosphate excess and possibly add a phosphate removal pad or medium to your filtration until it is significantly diminished. -but it's hard to guess what you're dealing with without tests and pure scientific method!
You must, above all, realize that a tank takes like 6 months to establish balance, nitrosomas, nitrobacter, and other factors. A truly stable tank that won't suffer many algal issues is one that is heavily planted and is a year or more old. Just give it time, please DO NOT give it chemicals.