Wow, I can't believe I missed this thread! I think the draining down in your case was an excellent idea, especially in Florida, sometimes it just makes it easier. The store bought test kit (and this is an agree to disagree thing) if used properly is as accurate in the tests it does (less than "5" as it really only does TA, pH and OTO chlorine) as the Taylor kit is (it's the "Poolmaster kit" relabeled as so many places do, like Ace and Home Depot.). I like the TA test better in that kit. (agree to disagree.) So, use it as a second test source when you are doing your weekly detailed tests, after this is over with. Having two sets of results from two kits for me verifies that I didn't screw something up in the testing process.
Not knowing CYA or CH makes that kit incomplete enough that you can't balance saturation though, so those really have to come from the Taylor kit.
The levels of Cl- and bleach would hurt your pool long term at your SLAM levels, but it's okay short term. Stuff moves on the scale of days to weeks in a 8.4k volume of water. You will learn that some of this stuff just isn't going to happen overnight!
Now the reason that the TF-100/K-2006 is pushed here-- is because there is one less MAJOR variable for people to help you on this board. But so far it looks like you are picking all of this up really quickly. If you follow the guidelines here after you get it under control, it will never happen again. Pool store testing is unreliable because the testing process itself has to be well controlled.
OTO chlorine tests only work to about 5-6 PPM. You can dilute the sample down maybe to at most 60% distilled or RO water to 40% pool water and read more. (easy to do on the Taylor kit, fill to the top of the second square with pool water, then the rest RO, and divide what you see by 0.4) If you are over 10 PPM or so, then the pH test isn't accurate. This would be on either kit because basically the chemicals are the same. The Taylor Safety kit has the chlorine neutralizer built in with the red pH chemicals, but otherwise they are the same chemicals in different concentrations. If you really want to trust the pH I wouldn't worry about it until the chlorine FC/CC is under control, or go and buy an electronic meter. If you are killing and filtering out the algae then keep a close eye on the filters until your are done.
The DPD test is far more accurate, as you can tell and can read SLAM values. Doing the diluted test OTO is good enough for spot checks and will save some money and is a little faster to do. It's not an official number to use on this board though, ever.
Soda Ash is Sodium Carbonate is Washing Soda. Baking Soda is Sodium Bicarbonate. Both are called ph UP on the commercial stuff at much higher cost. Obviously both are not the same in there effects. Play with effects of adding every chemical in Pool Math. Some will surprise you!
The zen of all of this is to use as few of the simplest chemicals as possible. I think you are well on the way to figuring it out. Best of luck!