The demigods of this world are avatars of the one true God known as Dea and built in the image of humanity. They are independent and have their own opinions from each other, but are connected by a universal consciousness that operates similarly to a hive mind. This "super-consciousnesses" underlies their actions and governs them according to a set of universal laws, which they are instinctively aware of and cannot break. This prevents them from interfering with the mortal plane in most cases.
These demigods breed differently from mortals. When a man and woman get busy, they produce an offspring which shares half of their parents DNA. These influences gene expression and creates a completely new individual. Demigods breed by leaving their physical avatars and combining their souls with each other to create a new soul. Every demigod currently alive will participate in this process together, causing the resulting offspring to have literally hundreds of "parents" who are also their siblings. Outside blood are not brought into the gene pool, with each new member coming from inside the family.
The problem lies with the fact that due to their breeding methods, every god is closely related (Mothers, fathers, sisters, brothers, etc). The resulting issues that comes along with incest is well documented. The greek gods also had incestuous affairs, with them marrying each other, such as Zeus and Hera. The inbreeding led to sociopathic infighting and family conflicts which drew humanity into pointless wars, as well as physical deformities, such as Hepheastus. This eventually led to these worthless and pathetic excuses for deities being destroyed by other competing gods or each other.
With these demigods, Dea wants to avoid this outcome. Even though all avatars will have a hand in creating new gods, each god's genetic build is unique to them. How can I make this work?