PSA Unclaimed SSS Expedition Eggs (Xeno Arena)
Tldr: If you have any unclaimed eggs from past expeditions, they can be rerolled to SSS. Just set a restore point, claim & hatch the egg, check stats, reload of undesirable.
This works with most expedition eggs, notably the Mecha-Mouse (mechanical), Appalling (toxic), Construct (mechanical), Robo-Warden (mechanical), and Helios (anomalous). This does not work with the Quad (mechanical), Sandworm (desert), or Whispering (toxic) eggs.
Re-rolling stats to SSS is also not a simple 1/64, as each stat class has a range of potential values. These values can be checked in your companion roster when initiating a battle (Oceanus is conveniently close to the Quicksilver Synthesis Companion). For example, my Mecha-Mouse had S class values in combat potential ranging 197-180, agility 93-62, and health 783-535. There also seems to be some overlap, as I once rolled an A class agility stat of 72, which is well within the range of S class. This led to some frustrating SAS, SSA, ASS rng.
So to all those who have waited for companions to be more than window dressing and left their unique expedition eggs untouched, I say happy hunting!