Approaches that come to mind of how they could design reincarnation:
1. Fixed, generic bonuses (like what it is now). Boring but effective.
2. Choose your own generic bonus, the points example above. Let players customize to their preferred playing style.
3. Fixed bonuses that vary by faction. Take whatever the faction does and start adding multipliers. That could be hand-coded for each faction or a flat bonus, say +10% to multipliers per reincarnation.
4. Accumulate bonuses per reincarnation. My mental model here is Kingdom of Loathing ascension: pick one thing from your current class and make it permanent. That may or may not be too strong; Kingdom of Loathing has a comparable number of classes and abilities and seems to be doing okay with letting players accumulate.
5. Hybridize the above.
Personally, as an old KoL player, I’m fond of 4. I would prefer something like 2 or 4 just to add a bit of personal customization, versus fixed bonuses where all that matters is how many reincarnations you have.