I've had problems with GHA off and on since day one. Your P04 and nitrates are so low becasue the GHA is absorbing them faster than your test can read it. Even though you may not want to think about it, if the only filtration you have is a hang on filter and skimmer, you may want to think of an upgrade to trickle filter or sump with a better skimmer, or possibly a canister filter.
The one thing that worked best for me is to set up a refugium with some cheatomorph algae in it. The chaeto will outcompete the GHA for nutrients and the GHA will gradually starve off. The refugium doesn't need to be big in size. I have a 75 gal
display tank and put the cheato in the bottom of my trickle filter in an area about 7 1/2 but 9 1/2 inches with a basic plant light I got at a regular department store behind the filter. I haven't had any GHA for over a year now.
Another option I've had some sucess with (but not as much as the refugium) is to get a product called Algaefix made by API. You'll hear mixed results from other people but it worked pretty well for me. Just follow the directions to the letter
and be sure to get the marine version. I used that first to to kill off the GHA then used the refugium to maintain.
If you use the phosguard, it works best in a phosban reactor. I tried that and it worked well but don't use it if you have leather corals.
My leathers didn't open up for at least six weeks after I stopped using it. You can also try Phosban which is a different material than the phosguard but has the same purpose. In my experience, it's easier on your leather corals too but doesn't seem to last as long.
I've been where your at too and I know the frustration. Hope this helps.