Wait, what? From what I can tell (unless I've misunderstood any part of this, which is very possible), Gendalla is about 36LY from Nefertem, where the "Thetis" is currently drifting. From what I understand, they encountered the strange signal 15LY from their current location (Nefertem?)... not 15LY from their departure on Sol. Right?
No, it was 15 LY "behind" wherever the ship was when the incident occurred. Which, as I said, was almost certainly not where the ship currently is located. The ship didn't suddenly stop dead, just because everybody on it died. It would have kept flying.
Here's my rough timetable of events.
Year 1: Thetis launches from Earth, in general direction of Nefertem.
Year 93: Thetis passes near Gendalla, doesn't stop but somehow picks up death-meme message, which is stored in the comms system.
Year 165: Thetis passes near the three starsystems of the Abrogo Cluster. Doesn't stop. There's a huge, star-less void between Abrogo and Nefertem.
Year 168: Thetis log events: death-meme escapes comms system and infects ship. Event happens in deep space while ship is still travelling at 0.2 c. Everybody aboard ship dies within a year. Ship continues outwards at 0.2 c, on autopilot.
Year 267: Thetis, now a ghost ship, arrives at Nefertem; autopilot decides to stop ship in Nefertem, despite lack of colonizable planets.
The events at 93, 165, and 267 are fixed, set by the cold equations of physics of where a ship will be when travelling in a straight-ish line between Earth and Nefertem at 0.2 c. The only variable is the actual infection event that I've put at 168; it might have happened later, if the crew were slower to procreate than I predicted. But if the "first ninth generation baby" didn't happen until Year 267, that means the parents waited until they were (on average) over 33 years old, which seems unrealistic on a ship that's specifically designed to be baby-powered.
The only other alternative theory is that Abrogo itself (or one of the other two starsystems in the Abrogo Cluster, being Yin Sector GW-W c1-26 and LHS 2149) is the source of the death-meme message, meaning the message was encountered somewhere around Year 165 and the event happened in around Year 240. Which I would deem unlikely, due to the same timing problem I mentioned above - the "generations" would have had to have been 30 years apart.