I dealt with that exact same algae problem with my tank YEARS ago.
The only thing that ended up fixing it was heavy filtering with a GFO reactor. The mats of algae would die in waves, and to help get the PO4 out further, I would go in and spend an hour or so peeling the dying algae off in large strips. It took several months of this, but I eventually eradicated it, although it did kill my clam, starfish (and spawned leg) and Goniopora in the process.
You can see it here:
What it would look like as it died... sort of a melting effect
Bucket o' crp
Holy crap... i have been dealing with this for almost 2.5 months now... To read your description of peeling it off is exactly my experience. I could go to one side of the sand, peel like tape and just get 2-6" of this crap.. it's heavy, smells awful, and I would have a bucket just like yours..
To the OP... I have waited, waited, and noticed that doing weekly water changes actually made it worse. So I have stopped and haven't done a WC in almost 5 weeks now. It got so bad, all my feather caulerpa in the fuge was choked out and basically couldn't even grow. What helped....
Not sure 100%, but I dosed a full bottle of Microbact7. Part of my sand after the bottle was done became white... I tried Seachem's Stability which took care of another part of my sand. I spent days in a row (in the morning or late evening when lights were going down) and peeled this crap off of my sand, and rock, wherever I saw it rotting and just dying. I literally pulled out lbs of this garbage... It started not coming back from my sand, and more of my sand was white... finally! I let my skimmer crank away and rip out nasty gunk constantly.
For this period of time, i ran GFO & Carbon in a BRS reactor constantly, changing it religiously and spending a bunch of money along the way. It didn't help.... at all. I tried purigen in the sump to keep nitrates down, and even chemipure elite. I was at my whits end.
The last straw, and I think it's getting to the final stretches of this, but I built this cage of eggcrate and actually added a small koralia into the fuge. I got some chaeto from a local reefer, but it into this elevated cage, and pointed the powerhead at it.. In the past, when I tried chaeto it would just get choked out by cyano it was so bad... it died.... it was that bad.
I have had the chaeto in there since last night around 5PM, and I woke up to seeing a part of one of my rocks that i haven't literally seen in 2.5 months... it's starting to recede in a bunch of spots, so my guess and observation is the chaeto might just be soaking up these phosphates..
So at the end of the day, don't give up, keep fighting the good fight, and you will be rewarded... This is my dream 150G tank, and I have lost some fish, SPS along the way.. Don't give up, fight it, and just remove as much of it as possible. As much as I think GFO\Carbon are great, physically ripping this crap out is huge.. There are spots way in the back that I just can't get to, so it's sitting there, but this morning I noticed it receding. Good luck...