There are 2 different level flowers that can potentially drop this organ, one in the Grand Palace and one in the Gardens. A BLU friend of mine said he never saw an organ drop on the lower level ones in the Palace while he was trying to learn his spell. So, I decided to try the ones in the Gardens, which has a higher listed drop rate on the Wiki.
Out of the 32 Aw'euvhi I duoed in one farming session, I got 4 NQ organs and 2 HQ. On a previous farming session (not sure how many I killed) I saw only 1 NQ and 4 or 5 HQ organs.
As a SCH, 3 Parsimony and 1 Ebullience T4 spells will kill the Aw's or leave just a tiny sliver of health left (954 Blizz4+Hailstorm, 884 and 1112 Thun4, target INT varies with level). The 16 minute respawn requires you to move to one of the other camps or wait for respawn (there are 6 camps with 2 flowers each that can be farmed in a circuit on the first floor, look for small L-shaped rooms).