At the moment I have a 180 gal tank with a dozen Andianoacara. Because they were all added about the same time, territorial disputes were relatively mild, although the alpha male drove 3 similar sized males right out of the tank.
View attachment 1364629
So consider what your alpha owner of a tank as small as a 75 gal,(i consider a 75 a relatively small tank for anything but the smallest cichlids) will do to a cichlid it considers a new interloper and competition.
In truth, I consider my 180 small, and plan on reducing the cichlid population.
I believe if you had added the cichlids all the same day, they may have worked the tank out, but add one and giving it enough time to establish sovereignty is a recipe for getting either the new one, or the GT (if not tough enough) killed.
Let us know the outcome, if you decide to tempt fate.