Ship experience/veterancy/personality comes in form of special hullmods. They can be only picked up at certain "random" moments, which would be
- event triggered, e.g. suffering heavy losses, making in-flight refits, getting close to a black hole...
- but not reliably so, there's just a small chance for any given trigger
- overall very rare, maybe with a hidden timer after one event
- not mandatory, you can refuse to install them
- more flavorful than other hullmods, more side-grades than straight upgrades
- an, to tie it in with a crew Event system: the best of these special hullmod events only pop up if you have experienced crew
- Over a long time, a ship might even accumulate several of these hullmods, really making it unique
Some examples:
Spoiler
Forged in Blood
The recent, traumatic battle has forged an unspoken brotherhood between the surviving crewmembers of the ISS Derringer. They ask permission to paint their hull blood red. This will set the ship behavior to reckless and increase weapon damage by 10%. Will you grant permission?
Spoiler
Out through the backdoor
After almost losing core containment during the last fight, the chief engineer of the ISS Brazen had to come up with a rather creative solution. The flux vents are now connected through to the engine, increasing forward speed by 50% during active venting - but flaming out the ship when the flux bar is full. The changes could still be reversed - will you allow the engineer to make them permanent?
Spoiler
They have seen the light
After some of the external shutters failed to close, the recent dip into a solar corona has left a permanent impression on the crew of the ISS Reinhold - or rather, on their retinas. Their auto-firing accuracy has dropped by 50%, but they have taken it upon themselves to install and maintain, in their own time, almost religiously, a solar shielding variant that is twice as effective as the normal one. You could order your surgeons to replace the blinded eyes against their owners will, but that would surely rob them of the will to maintain their hull modifications. Will you let the current condition persist?
Using hullmods seems both simple to understand for the player and gives a lot of storytelling opportunities. I can't think of a more straightforward alternative, at least.