in general, going a chemical route to fix something is not ideal. if you can beat it without going with routes that may or may not cause harm, then you are better off.
i ran into a GHA issue a while back and after coming to these forums, and doing my own research, i found that fixing it wasnt going to be a quick thing.
a few things i found is that manual removal is going to be required. i wouldnt use peroxide, because peroxide also kills bacteria. if you go that route, you cannot do all of the rock at once, otherwise you will run into other issues, so its just easier to go without that.
GHA grows with food and light, so you have to do something to change that. i found that a refugium, carbon dosing, and manual removal worked for me. when algae dies, it creates food for more algae, so if it isnt removed from the tank, it just continues with the cycle. the refugium gives algae a place where you want it to grow, and helps keep it out of the tank. carbon dosing helps remove the food that it uses to grow. the biggest thing that helped, as others have said, is manual removal.