Okay, here goes. This is even more complicated than I was realizing since you need low values for inducing a failed save (11 or lower) and high values to generate a hit (10 or higher), but these ranges overlap.
So the relevant bins are: 1-9, 10-11, 12-19, 20
Case 1: Two 1-9s: 0.45 * 0.45
Case 2: One 1-9, one 10-19: 2 * 0.45 * 0.50
Case 3: One 1-9, one 20: 2 * 0.45 * 0.05
Case 4: Two 10-11s: 0.10 * 0.10
Case 5: One 10-11, one 12-19: 2 * 0.10 * 0.40
Case 6: One 10-11, one 20: 2 * 0.10 * 0.05
Case 7: Two 12-19s: 0.40 * 0.40
Case 8: One 12-19, one 20: 2 * 0.40 * 0.05
Case 9: Two 20s: 0.05 * 0.05
Case 1: Dissonant Whispers for 3d6, regular attack roll for staff: 10.5 + 0.55 * 7.5 = 14.625
Case 2,4,5: Dissonant Whispers for 3d6, autohit on staff: 10.5 + 7.5 = 18
Case 3,6: Autocrit on Chromatic Orb (better than DW + staff crit): 27
Case 7: Autohit Chromatic Orb (better than letting them roll for DW): 13.5
Case 8,9: Autocrit Chromatic Orb: 27
Expected Damage: (0.45*0.45) * (14.625) + (2*0.45*0.50 + 0.10*0.10 + 2*0.10*0.40) * 18 + (2*0.45*0.05+2*0.10*0.05+0.05*0.05) * 27 + (0.40*0.40)*13.5 = 16.4