I see we've reverted to guesswork again and see what sticks. The following are known to be colonized between 2097 (departure of first generation ship from Sol per GalNet "
Galactic News: Generation Ships" from 19 August 3302). This means you have 199 years for Raxxla to be found between 2097 and 2296. Hyperspace doesn't become viable for humans even in a basic form until 2300. The Raxxla discovery, therefore, happens solidly in the pre-hyperspace era. It is therefore reasonable, that the search should be in or near the following:
Settled before 2296:
Sol (Permit-locked)
Tau Ceti - colonized approximately late 2116 - Mayflower 97 traveled at 0.6LY/year - self-sufficient by 2159 (Permit-locked)
Delta Pavonis 2190-2230
Beta Hyrdri - 2190-2230 (Permit-locked)
Altair - 2190-2230
Achenar - mid-2200s (Permit-locked)
Facece - (colonized shortly after Marlin's Republic founded in Achenar) (Permit-locked)
Also, do you notice a pattern here? A very sizable number of these are permits. All the following can be confirmed via tourist beacons or Codex entries.
Perhaps we should be starting here. Also, Marlin Duval died the same year Raxxla is found per Elite Encounters RPG (coincidence - probably not). Since, this was pre-hyperspace pretty much only these systems or their immediate neighbors are candidates.
One last side note: Marlin Duval may not have died in Achernar. The system Capella has bodies by the name of Duval's Grave and Lawrence's Grave (I've been there personally). Now, there is no tourist/visitor beacons there to confirm which of the Duval lineage died there but it and its neighbors should likely be under consideration, too.