I get what you're saying mate. But Barzini would have read the body language of Mike at the Funeral, not even a nod of thanks for Barzini's attendance, second, surely Barzini would know that Vito would warn him that the man who came to him with a meeting proposal is the traitor. Barzini didn't care about throwing Tessio to the lions...but never would Barzini leave himself open to such an attack in broad daylight.
This bad mood acting was part of the trap. If Michael appeared to be too friendly towards Barzini, Barzini would have smelled a rat.
In the novel we find an interesting part about this irritation, when Clemenza prepares to have Paulie killed.
He would be curt with Paulie, as if displeased with him. With a man so sensitive and suspicious as Gatto this would throw him off the track or at least leave him uncertain. Undue friendliness would make him wary. But of course the curtness must not be too angry. It had to be rather an absentminded sort of irritation.
Barzini knew that Michael knew that Barzini chiseled into the Corleone territory. When Michael acted stiffly, it was only natural.
