Vito should have figured it out a lot earlier. He tells Tom, after the meeting, "Tattaglia is a pimp; alone he could never have outfought Santino." Well, Tattaglia was always a pimp who didn't have the balls or the resources to fight alone. Why couldn't he have surmised that Barzini was behind Tattaglia?
I think you're expecting a lot of Vito.
He clearly suspected that there was someone behind Tattaglia but didn't have any reason to suspect Barzini over the other Dons until the meeting.
While it's been said that Barzini, as the second-most powerful Don, was the most likely candidate, that's not a compelling argument to me. Any of the other Families would have jumped at the opportunity to gain the wealth and power that ruling the drug trade would have gained them.
Vito knew this, and he knew that a mistaken guess as to his adversary would be disastrous. So he arranged a meeting where he could observe all his suspects and see if one fell into his trap. Barzini did, and this allowed Vito (and Michael) to win the war.
The Don wasn't slippin.
