I'm surmising that Tessio had made up his mind not to go with Michael after the fishtank scene. I don't believe he would have approached Barzini with a plan until Vito died. Tess may have had scruples about loyalty to Vito. He may have hoped that Vito might still take his side and influence Michael. Or, more likely, Tessio, "always smarter," would have seen that it would be dangerous to approach Barzini before Vito died--what if Barz thought it was a plot by Vito (a la Luca/Tattaglia) to suss out Barz's intentions? An approach after Vito died, with "weak" Michael in charge, would be less suspicious.

1,2 and 3 all happened before the Commission meeting and the peace agreement. 4 was not covered by the peace agreement. Nor was 5, if it was even true that Moe "talked to Barzini."