The real test to see if it's time to let your chlorine drop is to test after the sun is off the pool, and again in the morning before the sun is on the pool--if you don't lose any chlorine in that time, then you can let the chlorine drop--but in your case, do NOT let it drop below 5, and I would keep it closer to 7 or 8 ppm. One day in the sun will probably accomplish this. You do still need to be working on your pH, though--anything below 7.0 is acidic and can do damage to your liner. I think the reason you're having trouble getting it to move is not due to the alk, but rather that it was far lower than you thought, and it's just taking a lot of Borax to bring it up. If you want, you can use Washing Soda to bring up both TA and alk at the same time. Or, if you already have them, continue with the Borax for pH and you can add baking soda to bring up the TA.

I would not use the "clean and sweep" stuff that you have, if the water is clearing. You'd be better off to just be patient and let the filter do its job. Remember that the chlorine killed the algae, but the filter is what's going to get it out of the water. The floc that you have might or might not speed up that process, but it may also cause you other problems, too. I would just let the filter get it. If the algae is dead, and the chlorine drops a little, the only real danger with swimming in cloudy water is not being able to see somebody underwater in the deep end if they get into trouble--so make sure if they swim before it's completely clear, that you keep a really good eye on anybody in the water.

Janet