I don't think you are adding enough bleach at a time. In a 5900 gallon pool, each quart (32 oz.) of 6% bleach will only increase the chlorine level by 2.5ppm. Adding only 12 oz. at a time isn't going to give you much chlorine ---- especially since with no CYA in there, it is going to quickly be lost to the sun. I think you better start adding larger doses of bleach at a time or your freshly filled pool will soon turn green! It doesn't take long for that to happen. My suggestion is to add a 3 qt. bottle of bleach which will take it up to about 7.6ppm, but it won't stay there long. In a matter of hours, it will fall. Test it around 3x per day if you can and each time add enough bleach to get back to around 6 or so. Doesn't have to be precise. After you start to get a CYA reading, you should be able to test and dose in the evenings only.
To answer a few of your questions, you can test the chlorine a couple hours after you add it. You can add the CYA to a sock and hang it in front of a return. I don't think I'd hang it from a metal ladder. It is probably best to leave the pump running while the sock is hanging to speed up how fast the cya will dissolve. You can also give it a squeeze a couple of times a day as that will also speed things up. Another method for adding it is to add it directly into the skimmer (slowly) and let it dissolve in your filter. That is what I do. After doing so, I usually run my pump 24/7 for a couple of days. Also, don't backwash the filter for up to a week or else you'll just throw the CYA out with the waste water.
You are ok with pH of 7.8 but no higher. I'd wait a day or two and get a couple more readings. Adding the CYA may cause it to come down a little. If after a few days it is still reading 7.8, you might want to consider using a little muriatic acid to lower it. But, let's just wait a bit on that.
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