I am with you on avoiding miracle mystery chemicals. But fluconazole is safe. My LFS uses it on customer tanks that get overgrown GHA or bryopsis. No SPS, LPS, softy mortality. Instructions are simple.
It is used to treat fungal infections in fish, but it also does a number on bryopsis in particular and GHA over time. There are several professional aquaculturists that actually dose it continuously to replace the amount removed by WCs. Seriously.
It WILL NOT prevent GHA from returning once it is removed via WCs. As
@Phildago says, there are many methods/tools for controlling your nutrient levels once you knock this back.
a) Dose Reef Flux now. Follow the simple instructions.
b) Order Hanna ULR Phosphate Checker now. (Useless until you kill the GHA; vital thereafter.
c) Order a quality, low range nitrate test kit. Red Sea is good. (Again, useless now but vital later.)
d) Do some research on nutrient export methods & tools.
e) Choose your tool set and measure your nutrients every 3-5 days in the beginning so that you don't completely strip the water. Phosphate is stored in the rock, at will continue to leach out for a while until exhausted.
f) Aim for 5-10 nitrates and .04 to .08 phosphates