I'll tackle the Alleged Barney position first, He would have come out of the Vito Genovese line by Coppola crew and virtue of being blessed by Vinnie Chin.

Sceond, the power that Costello wielded was partly because Luciano was still in the picture in the late 40's when Genovese returned to U.S. Once Willie Moretti who was Costello's muscle got clipped, the power within started to shift back to Vito
the main players
Costello side:
Willie Moretti/Jerry Catena
Joe Adonis/Jimmy Blue Eyes Alo
Little Augie Pisano Carfano
Joe Socks Lanza
Genovese Side:
Tony Bender Strollo
Trigger Mike Coppola
Mike Miranda

On the fence guys:
Tommy Greco
Rocco Pellegrino
possibly more