How about this for the first 41 games (in parentheses are the guys who are the first guys up in the pen: M-miley, A-ashby, H-Houser, L-Lauer--assuming they weren't used in the previous game or two, and they'd go 2 or more innings):
March 30: Burnes (A, M, L).
April 1: Woodruff (A, H). April 2: Peralta (A,H). April 3: Lauer (A,H) April 4: Miley (A,H). April 5: Burnes (A, H). April 7: Woodruff (A, H). April 8: Peralta (A, H). April 9: Lauer(A, H). April 10: Miley (H). April 11: Burnes (H). April 12: Ashby (H). April 13 Woodruff (H). April 14: Peralta (H). April 15: Lauer (H). April 16: Miley(H). April 17: Burnes (H). April 18: Ashby. April 19: Woodruff (M). April 20: Peralta (M). April 21: Lauer (M). April 22: Houser (M). April 23: Burnes (M). April 24 Ashby (M). April 25: Woodruff (H, M). April 26: Peralta (H, M). April 28: Lauer (H, M). April 29: Burnes (H, M). April 30: Ashby (H, M). May 2: Woodruff (H, M). May 3: Peralta (H, M). May 4: Lauer (H). May 5; Burnes (H). May 6: Ashby (H). May 7: Miley (H). May 8: Woodruff (H). May 9; Peralta (A, H). May 10: Burnes (A, H). May 12: Lauer (A, H). May 13: Miley (H). May 14: Woodruff (H).
Min 5 days off after a start (except bumped up Burnes once to avoid a day off). Burnes gets 8 starts, Woodruff 8, Peralta 7, Lauer 7, Miley 5, Ashby 5, Houser 1. Miley started in the rotation, cycled off for a couple of weeks, Ashby started in the bullpen, Weren't many opportunities for the 7th guy (Houser) but that could change if someone is nicked up and misses a start or two; Houser could get as much work as he could take as the first guy up. I think this could work. Could bump up Burnes or Woodruff occasionally.