The bacteria that are associated with HLLE prefer a pH between 7.2 -8.5.+/- a few tenths.
But so does the Andinoacara you keep, so pH is not the culprit.
The difference here, is that in natural waters where Andinoacara are found, nitrate levels are very low, normally non-detectable.
Although in much of the geneic aquarium literature, a nitrate level of 20 ppm is considered acceptable, because it doesn't cause acute disease or obvious death, yet I find (and much of the many disease posts here on MFK suggest) a nitrate level of 20ppm leads to chronic diseases like HLLE as fish like oscars, Geophagines, and other medium - large cichlid species age. It often doesn't present until the fish a 2 or more years old.
I keep wild caught Andinoacara from close to where I live in Panama (pH 8.2), and have yet to test the water they come from, and get a test result over 5ppm.
For this reason I maintain low nitrate levels of no more than 5 ppm in my tanks, and to reach that goal, I find I need to do 3 to 4 water changes of 30-40% on my 300 gallon system per week. When I first got A coerleopunctatus at only a couple inches, this regime may not have been necessary, but as they are now much larger (the male is @ 7", females slightly smaller) and their waste output is much heavier, my nitrate testing shows this amount and volume of water changes to be minimal to attain my goal of matching their natural waters.
Another factor in natural waters, is the seasonal leaf drop that inundates the waters with tannins (which are slightly antibacterial).
Below my average tank water nitrate results

My suggestion would be to up your water change routine until you bring those nitrates minimally below 10ppm, and keep that routine up, regularly measuring nitrate.
But....
not to expect an overnight cure or even visible change in just a month, the medication suggested is a good bandage, but the underlying cause is what is needed to keep the fish from relapsing.
It has probably taken some time for your GT to get HLLE, so will take time to get rid of it.
One of my Andinoacara below
Another factor in maintaining low nitrate is the addition plenty of aquatic and terrestrial plants, a much higher mass than the fish.

The main tank above, the planted sump below
