Someone with better actual Cichlid info can respond for mixing them.
Adding anything different to a peaceable situation is a possible negative outcome.
The Cockatoo Cichlids, Apistogramma cacatuoides, are generally easy going but if breeding, any fish can get testy and protective.
Is there any way you could house them into a breeding sized tank and they could live by themselves, and you could raise babies and sell them. Double Reds are pretty popular.
Traditionally aggressive, and especially larger Cichlids are likely too much for these smaller guys.
In addition, if the fish you have are not yet in their maturing /breeding age, you could still have problems in the future when the breeding behavior kicks in.