Frankie didn’t die in the bar because the cop walking a beat came through the front door.
I believe that the other family wanted to torture Frankie with the final thought before his death that the head of his own family had turned on him.
I'll disagree with you again, although I think you're right on target with most all of your other insights.
The screenplay shows Michael saying "How did they get their hands on Pantangeli?
Hagen responds "Roth engineered it, Michael. He made Pentangeli think you hit him. Deliberately letting him get off alive. Then the New York detectives turned Frankie over to the FBI...."