This quest is always available, anniversary or not. The only problem is, the parts no longer drop (until this Friday when the revamped zones they drop in go live again).
If you can find Athlai/Othni/Reis parts (in bazaar maybe), you can always turn them in to Thach. He's directly across from the Shroudkeeper near the parcel gnome (Caden Zharik) and the small bank.