Let's do the following.
1) Keep adding bleach, as often as you can test and replace FC to get back to 8ppm FC. Why? That is the top of the TARGET FC range for a CYA of 50.
FC/CYA Levels
Why, My CYA isn't at 50 yet? You added 4lbs of stabilizer yesterday, that is at least CYA of 20. You have another 4lbs in the skimmer that will get you to 45. For our purposes at this point, your CYA is effectively 50 (we always round up on tests/additions of CYA).
But, but, but isn't that too high? Pool, people and equipment are safe up to SLAM level FC. SLAM FC for 20CYA is 10. 7ppm is absolutely ok.
2) Let the CYA dissolve. Are you squeezing? Squeeze it until it is dissolved. We want to get to 24-48 after CYA addition.
3) I think, given the fact that your FC got to zero a couple time, you likely have algae. Even if the cloudy is gone and you can't see it. You will want to perform an Overnight Chlorine Loss test. Super easy and will tell us if you have algae. Print these instructions out. Read them three times, then execute and come back with results (click this link and print)-->
Overnight Chlorine Loss Test
4) Look at your test kit instructions for FC and CC. There are two tests. One that is a 10mL sample size (.5FC and CC per drop) and one that is 25mL sample size (.2FC and CC per drop). For our purposes, let's use the 10mL sample size. This is PLENTY accurate and will save reagents.
If ANY of this doesn't make sense, ask.