"When water is super chlorinated the material that the chlorine attacks practically falls out of the water onto the bottom of the pool...or at least that's the easiest way to explain it.."
A lot of the powdered shock treatments contain a flocculant, like alum. This binds the small particles together, allowing them to fall to the bottom in a still pool. Sometimes, I'd let my pool go green. To rescue it, I would super-chlorinate, add the shock and mix for a few hours, then let it sit without the pump going for a day or two. The water would be crystal clear, with the algae all clumped on the bottom. I then attached the pool vac hose to a 5 gal plastic pail, in which I had inserted a sump pump.
VERY slowly and gently, I would vac the bottom, removing the algae. The output of the sump pump went to a street drain and not back into the pool. If I had to guess, only about 100 gallons or less of water and algae would be removed. Trying to do the same type of vacuum treatment with the pool pump merely spread the algae throughout the pool again.
In reviewing the way pool pumps and filters clean a pool, it is a hit and miss operation. Filtered water gets mixed back in with the dirty water and while the percentage of water that is cleaned increases, without flocculants it can never get 100% clean.
If I were designing a pool, I'd want to try a design where a plastic sheet or bladder could be inserted that fit against the pool walls. Water from the pump would be pumped into the bladder or clean section, and once all of the water had gone through the filter once, the entire pool would be clean, and the plastic could be removed.
However, I'm done with pools. The stream in my backyard is fine for me.