dontomasso and mustachepete, you make some excellent points. Tessio would have been adjudged to have jumped the chain of command if he went to Barzini on his own and revealed as such. Even without Vito's advice, Michael likely would've judged the act of going to Barzini to be traitorous in and of itself, especially with the tensions between the families. My theory on it goes into uncharted areas and makes a few assumptions. It makes Tessio out to be a rather cunning individual. I find it hard to believe that an old hand like him would've made such a classic blunder, greed or no greed.

My take is that Tessio was trying to play both ends toward the middle, as it were, for his own gain. On his side, he has a Don who's green to the job (Michael) and seemingly incompetent. On the opposite side, there's another Don (Barzini) looking to muscle in and take over.

I believe that Tessio wasn't looking to form an alliance with Barzini, because he knew he couldn't survive as a traitor even if he manages to carry out the hit. By allying with Barzini, as an experienced criminal mind, he would realize that he's taking all of the risk here with potentially no reward in the long term; as you say, he's dead inside of six months. As such, he would then be looking to usurp Barzini.

He wanted to set Michael up to be taken out, and for Barzini to be the fall guy for it. The arrangements that he moans over were his own. First, he approaches Barzini with a peace proposal from Michael; next, he approaches Michael saying that Barzini approached him with the same peace proposal. If the meeting goes on as planned, Tessio has his own men at the toll booth laying in wait, playing it up as Barzini troops. The car is ambushed, Michael and his men are taken out and Tessio "survives" the attack. The attack is classic Barzini. The Corleones retaliate and take out Barzini. Tessio then steps into the big seat and takes over.

On the bit about the restaurant, it was on Tessio's turf, wasn't it? If the restaurant's reputation was well known, Tessio probably dined there quite a bit; if the toilet tank configuration was unusual for the time, it would've been notable.