I to, for the first time in 15 years, started to have a green algae problem just below the surface in my pool vacuum canister, about 8 inches below the surface. Otherwise the pool was free and clear of algae and sparkling with bottom clearly visible, I did have iron stains but I just dealt with that issue on Monday.
Like you I raised the level the level of my chlorine from my normal (for the last 10 years) 3 ppm at a CYA of 30 ppm, cleaned out the canister with one part chlorine to four parts water, but it slowly re-appeared. I then checked for nitrates (you can buy a cheap kit at a pet store) and sure enough it was quite high at 40 ppm or higher, usually 10 to 20 ppm. This I believe was the issue. Unfortunately the only way to reduce nitrate levels is to drain out the water, either all or some depending on the level you wish.
I also reduced phosphates from around 1500 ppm to 200 ppm, some say this is not necessary. The ppm of phosphate will also go down when you drain or you can use phosphate remover. Some people also believe phosphates over 1000 ppm will help feed the algae. The jury is out on this, some say this is just an expensive ploy on behalf of the pool supply companies, others stating it to be necessary. I am not smart emough to comment on phosphates.
At your CYA level, Chlorine level and pH, assuming your Calcium is around 300 and your Salt is around 3200, it should be near nigh impossible to get algae as your your HOCL (as ppm Cl2) is 0.107 twice the recommended norm of 0.050 according to the PoolEquations spreadsheet. Or in other words, at that level it should kill about everything living in the pool super-quick. Nitrates are in all probability your issue. When was the last time you drained your pool?
When we drained my next door neighbours pool his water was clear, we got the numbers right and shocked the pool for a week prior to draining completely, he did have black algae because for 17 years it was not maintained correctly by his pool service, nor was it ever drained. When we did drain it, after a stain treat, despite the water being clear when drained and holding chlorine at 5 ppm at a CYA of 30 ppm, at the point where we got down to the last 25% of the pool water it started to stink like a fish market, and I mean bad, really bad; great for the garden though if it were not for the salt. So the story here is that appearances can be deceiving.
I think nitrates or possibly really high TDS for reasons of non-drainage might also be your issue.
If it were me I would shock at very high levels for 4 days to a week and scrub, scrub the walls and floor twice a day for a week. If you are planning on draining completely (recommended if you have not drained for a very long time), or drain down, by the percentage needed to get to 10 ppm of nitrate, if you do have nitrates, and then shock.
I used live in North Atlanta in the "burbs" and if your yard/garden was anything like mine I had lots of trees and bushes just waiting to fill my pool with nitrates from their leaves (although I did not understand the realationship betwen nitrates/algae/pool water at the time). I loved living there, so green, great climate, rolling hills and at that time over 22 years ago not too much traffic, I hear that changed, the traffic I mean.
Hope this helps.
