Memories get cloudy over time. Apparently there's no photo of the Facciola guy with the canary in his mouth. It's the cigar guy I am remembering, and he did indeed make the front page of the papers. I thought the canary incident was also older. Also I am probably confusing Paul C with someone called "the gentle don" from Philly. Nice little yawning photo of that guy as well, though I don't remember it.
I do remember now, from a documentary, that Paul C had become a weak boss and naively trusted Gotti, and that Gotti was nearby, not the shooter. I remember Gravano, think he got relocated to Arizona under witness protection but came out voluntarily years later.
As for Gotti, I think they changed some racketeering law or something just to be able to make charges stick. He was called the teflon don after all.
I will look for the CP angle you mentioned, though I have trouble believing those old Italian NY mobsters ever would have put up with that. They preferred the clean stuff, like drug dealing, making people pay for protection, trash collection monopolies, etc.