You've cleared up a LOT, just with chlorination and filtration. I'm a little reluctant to start you on a process that may clear up with water faster, but leave you with a lot of dissolved iron to remove from that water.

If you're getting reddish brown sediment on the filter, I'd be inclined to keep chlorinating and filtering. If you're not running your pump 24/7, do so.

You probably realize your pH and alkalinity are high, and your calcium is high-ish. If you want to try something, that may help you accelerate the iron clean-up AND fix your calcium and possibly even your alkalinity level, I'd suggest doing that, than using all the other stuff. You can use those things later, if you have stains, or next year, when you fill.

Here's what I'm talking about. Your pH, alkalinity and calcium are high enough to precipitate calcium carbonate. In fact, I'm guessing that's already happening, as aeration pushes your pH up. That calcium carbonate is forming slowly enough so that it's being filtered out . . . and probably taking some iron with it. The conventional thing to do would be to lower the pH and alkalinity. But, that's going to re-dissolve some of that iron. If, instead, you ADD alkalinity, you may be able to drop out even more calcium carbonate AND more iron. Doing it that way will remove the iron from your pool, with no additional steps. You may STILL find, once the pool's completely clear, that you have stains. If so, we can back up and remove those.

Regardless, do these things:
1. Use dichlor, not bleach to maintain chlorine levels in the 1 - 3 range. That way, you are adding BOTH chlorine and stabilizer.
2. With a PF of 27, a bottle of polyquat contains 1.4 lbs of 100% polyquat x 27 or 38 ppm in your pool. An effective dose is 2 - 3 ppm, or about 1/4 cup. Use this every three days, till the pool is clear. This will ALSO improve filtration.

If you want to try the alkalinity removal technique, buy a box of Arm & Hammer Super Washing Soda 55 oz at Walmart. Collect a sample of pool water in the largest clear glass container (like a water pitcher) you have. Add a tablespoon of washing soda, and mix. If the water gets cloudy, you're in business. What you can then do is add 2 cup doses of washing soda to your skimmer, in the evening, and leave the pump running all night. What you should see is a filter that's stopping up or filling up quickly, with a combination of calcium and iron. Every time you clean it, you've removed some of that stuff.

Cautions:
1. If you find that the pool is still cloudier in the AM, after running all night, skip a dose the following night.
2. After two doses, retest your pH, calcium and alkalinity, to see how they've changed.
3. You'll probably get some sediment on the bottom that you'll need to vacuum. (You probably already have some, but this will add more.)
4. Add a cup, in the first dose, and wait 30 minutes before adding the 2nd cup. If anything EXCEPT the water getting cloudier, happens, skip the rest of the dose and let me know.

Also, please fill out the pool chart, so I know a little more about your pool:
Pool Chart Entry Form
Pool Chart Results
Mainly, I want to know what kind of filter you have.

Also, I looked over your chemical list. We'll figure out how to use those things up, later. But, don't use ANY of them now.