Here's the thing though if Vito hadn't died when he 'conveniently'! did?

Are you saying Tessio-Barzini deal / Barzini-Michael meeting were all arranged and cemented only between Vito's death and funeral

Barzini didn't wait until Vito died before He moved against him when he was alive
1. sanctioning killing him
2. killing Sonny
3. car bomb attempt on Michael
4. chiseling Tessio's territories
5. backing Moe Greene