Consider MEXICAN turbo snails. They are bigger than the others and can push things around. Notwithstanding, they eat and eat and eat. I would suggest getting a dozen. Then, when the job is done, give a few of them away. At that point you will need to find a balance that sustains them. When I had cotton candy algae (pink poofy stuff), I got six until it was gone. Now I have 3 - 1 in sump, 1 in over flow, and 1 in main display. The one in the over flow seems to go back and forth.
When I had a bristle tooth tang, I have zero algae problem too.
As for source, it is also possible that it is coming from your rocks. I have rocks from Florida which are the same as Marco's rocks and look similar to yours. Florida has got to be one of the top exporters of phosphate in the state. There is a reason for that... Anyway, with time, the calcium in the rock dissolves. And in the process, it can open up deposits of phosphate on the rocks which will release phosphate into the tank. Unfortunately, it can also be absorbed back into other rocks. As a result, even if the deposit is consumed, you will then have to wait till the phosphate leaches back out of the other rocks.
Be mindful that the snail poop must be exported via your protein skimmer, water changes, or refugium.
A friend of mine how uncontrollable hair algae. Worse yet snails would die in his tank. The assumption was that the rocks were leaching phosphate and copper. After a while, it passed. He also had a very fat yellow tang.
Hopefully this is something that will pass with the help of some Mexican turbo snails.