The best thing you can do to help us help you is to stop using the strips and start using the HTH kit. Strips simply are not reliable or accurate enough to clear up a problem.

Stop using the algaecides and clarifier--they will tend to make your problems much worse instead of better. In fact, once you throw enough of the mystery stuff in the pool, then it's really hard to help get it straightened out because things start reacting unpredictably. Check the chlorine tablets you're using, and make sure that they don't contain copper. Adding copper will add another dimension of difficulty to managing your water. Also, we really need to know the ingredient in the "shock" that you're using, and a good set of current test results, taken with your HTH kit.

There are three reasons right off the bat that I can think of that will cause cloudy water that's not clearing: 1) you just need more time to filter out the dead algae that you killed off--and AGP pumps/filters are notoriously mis-matched, so it often takes a long, long time to filter out dead algae, and 2) You haven't killed off all the algae yet--which is a very big possibility given your water temps and strip testing, and 3) The "shock" you're using is actually cal-hypo, which is why we keep asking for the ingredient. Using cal-hypo with water already high in hardness and TA will cause milky, cloudy water. And....it's possible that you have all of those problems at the same time. So.....

In order to rule out algae that's not dead yet, you need to test your chlorine levels at night and again the next morning before the sun hits the pool. Compare the two numbers, and if you've lost more than 1 ppm of chlorine in that time, then we know there's something in the water eating it up and you need to shock the pool and hold it at shock level until you can go all night without losing chlorine. To do this, you're going to need an accurate CYA level, because your shock level depends on your CYA level.

To rule out calcium being the problem, you need to test your water for calcium hardness--that test is in your HTH kit as well.

Once you've determined whether the problem is in the water or in the filtering, then we'll need to look at your filter. Are you running the filter 24/7? Is the pressure rising on your filter as the pump runs? What, if anything is washing off the carts when you clean them?