After a similar research journey, I recently planted 3 elderberry shrubs (Sambucus canadensis) for this situation. The roots are shallow (2 - 3 feet) and mat-like. The plants do well in full sun which is a feature of most leach fields. The bare root plants will take 2-3 years to fruit. The soil
should be well draining which is the nature of a good drain field. Cuttings can be taken for new plants should the leach field require an overhaul.
Edited to add:
If elderberry roots find a source of standing
water (such as a broken lateral pipe or, in my case, the perforated drainage pipe), the plant will die of root rot. This could be a good thing.