I believe the possibility of the same problem between the Cuban, and managuense will also crop up with the friedrichthalii.
I would never keep two of the same genus (Parachromis, or a look alike such as Nandopsis) in the same tank.
You would not (or at least seldom) see those of the same genus Parachromis in nature together, because they are competitors, and this same problem is not alleviated in a aquarium, it is actually magnified because of the limited available space.
I have friends that are major Parachromis fans, and keep every Parachromis species of the genus in their tanks, but.... the long term successful of these Parachromic keepers is that, they do not keep different Parachromis species together, each species has its own tank, or is in a large enough community tank, with non-Parachromis cichlids.
I have also kept 2 Nandopsis species, and Parachromis at the same time, but like they did, not in the same tank. Probably why I always had 15 to 20 tanks running at the same time.
But this is not just a Parachromis thing, because in nature in any one geographical area, you seldom find 2 Vieja species, or 2 of some other genera together in close proximity.
In nature over time one species almost always edges the other out of existence. Thorichthys is about the only genus where you regularly find more than 1 species of Central American cichlid coexisting with the other, and this may be because they are innately social species.