Martinho lists everything I considered, but the one thing I think he missed was Ringworld Hindmost's engineering skill. No hindmost in Fleet of Worlds has that skill except for Baedeker. If it is another hindmost, then he has yet to surface, which would make little sense because Ringworld Hindmost points out his own involvement in earlier policies and programs. Particularly, Hindmost states that he helped develop the superconductor plague that destroyed the City Builders civilization. He felt what remorse from that I suppose a Puppeteer could possibly feel. Baedeker clearly was involved in that plot since he knew enough about the Ringworld to destroy the evidence of it prior to the Gwa'oth taking control of the Concordance. Also, Baedeker clearly is the better hindmost compared to Achilles. Lastly, Achilles is not a conservative, and never was one. Achilles would have no trouble leaving the Ringworld to fall into its star, and would not have been capable of exceeding the engineering and technical skill of a Pak Protector when guiding the flare at the end of Ringworld Engineers (really beginning of Ringworld Throne when Niven wrote that the Ringworld inhabitants did not suffer as great a loss).
It seems more reasonable to me that Baedeker eventually deposes Achilles, kicks the Gw'oth from the Concordance, and is then deposed by the Conservatives to make his way to Known Space and kidnap Louis Wu. The authors can do whatever they want with the plot, but I don't see any reasonable way to avoid making Baedeker one and the same as the Hindmost in Ringworld. One also should consider whether Nessus would produce offspring with Achilles of all people.