Humor me:
1. Finnegan (closer)
2. Harvey (highest leverage setup, alt closer)
3. Robert Hunter Jerry Garcia (lefty high leverage, 7th inning setup, lyrics and guitar solos)
4. Dylan Floro (7th / 8th inning)
5. Tanner Rainey (recovering, likely to start out in middle relief)
6. Jose Ferrer (groomed for high leverage but starts out in middle relief)
7. Jordan Weems / Mason Thompson (low leverage and middle relief, multi innings)
8. Joan Adon (long relief if not in rotation) / Trevor Williams (if / when a 5th starter enters the picture)
A level down
9. Thompson (or Weems)
10. Willingham
11. Rutledge (or potentially the long guy in the MLB)
Various Brzykcys, Henry recovering from injury, plus other minor leaguers who get hot.
Looking at that list, there's probably enough to deal off of the major league pen.