I have had pools over the past 35 years, but this is my first plaster pool. I had never had issues like this with my previous 2 pools, yet I experienced the same type of issues you are seeing when they finished my Wet Edge pool.
I followed the TFP method meticulously, yet had to SLAM every 4-8 weeks. We have very little bather load (just me and my wife), and have a screened enclosure over the pool. I scrubbed the pool more frequently, ran my cleaner more often, cleaned filters, and finally swapped out filters. I pulled my light and checked, then even tried Borates - all to no avail.
I started tracking my numbers more closely, and noticed that anytime my chlorine dropped below 8-10, the haziness would show up within days (note that my CYA levels are always kept around 70-80). A quick SLAM would clear it up again for a month or so.
About a year and half ago, I started keeping my chlorine above 8 at all times and found that I could go 3-6 months before I would experience the haziness. Those times can be easily explained - usually after a heavy rain that washes a ton of pollen off the screen and into the pool.
I've posted this issue several times on TFP some time ago, but never really got any solution. The recommendations are what I listed as having tried. Maybe it's just a mid-Florida thing... or I'm really missing something obvious.