Hello; I had ten tiger barbs with 5 serpae tetras, 4+ cherry barbs, 4 kuhli loaches, 4 cory catfish, several varities of zebra daino together for several years. The tigers control whatever area they choose to be in, but have not damaged the other tank mates. This combination has been fine forr several years. Don't know about neons with them as I have not tried that mix.
I have kept kribensis many times and feel they will do well with tigers. A male kribensis will very likely stake out a territory and defend it with help from a female if present. With over 75 gallons, unless it is very deep, there should be ample room for this and space left over for the other fish. They will chase other fish out of an area. They will also dig a nest in the substrate, generally under some form of structure. I would likely put some sort of structure in opposite corners and let them pick. This might limit the territory to one part of the tank. A pair are likely to mate in a community tank. You can also keep rooted plants with them as they do not up root them like many other cichlids