I think that Paul's suggestion of Gotti, Tommy Gambino and Bilotti ruling as a three man panel was Paul's attempt at blowing smoke up Gotti's wazoo. Paul knew that Gotti was ambitious and tough,and he thought that if he indicated that Gotti would get a seat on the ruling panel,Gotti would play nice.

That way Gotti would be happy and when the time was right,Paul would have had Bilotti whack Gotti.Then it would have been Tommy as Boss and Bilotti as underboss. Paulie was looking at the typical Gambino setup that had worked so well.A strong Boss,and a ruthless and feared underboss.

You had Carlo/Neil,then Paulie/Neil.
Castellano was so out of it that he thought Bilotti would be the Dellacroce to Tommy Gambino.He never understood that Bilotti was not as respected or feared as Neil,and never would be.
I don't think there would have been a war between Tommy G.and Gotti,because i don't think Tommy wanted to be boss. He had a nice gig in the garment industry and could care less about the other BS.
I think he would have stepped aside,Gotti would have killed Bilotti,and Gotti would be then Boss.