The gryphons fix themselves exactly 5 minutes after you ask Inquisitor Cleardawn to send the signal. At the 5 minute mark, gryphons 2, 3, and 4 will phase, and 2 and 4 will become non-interactable. You can tell they are "ready" when only gryphon 3 is interactable.
I've tested this quest like 20 times tonight and I personally found no correlation with anything else I tested.
Things I tried that had no effect:
- reloading, relogging, and relaunching WoW
- using the Throw Liquid Fire ability before clicking a gryphon and before talking to Inquisitor Cleardawn, thrown both away from NPCs/gryphons and at them (via Ishmalara in eadierlam421's comment)
- killing the exact amount of Witch Forces needed and no more
- killing the last required Witch Forces within the Crimsonwood Demolisher auto-exit area at the northwestern ridge
- triggering the auto-exit while the Demolisher was in combat, not in combat, at full health, and not at full health
- using only the Demolisher's Slam ability, ignoring Stomp and Speed Up
- manually exiting the Demolisher before entering the auto-exit area
- clicking gryphon 1 while it was still interactable (this is the only gryphon that phases correctly, and becomes non-interactable once it lands)
- mounting and dismounting while gryphons were bugged
- talking to Inquisitor Cleardawn, Warren Ashton, and Marten Webb between clicking the gryphons
- clicking all four gryphons multiple times
- clicking one gryphon repeatedly (I gave up after 60 failed clicks)
- clicking none of the gryphons (still phase automatically after 5 minutes)
On an unrelated note, be careful abandoning and redoing Stick It To 'Em! after the gryphons have fixed themselves. If you do so without taking the debugged gryphon to Arom's Stand, you're likely to get disconnected a few times when you try to take control of the Crimsonwood Demolisher. Abandoning and redoing Stick It To 'Em! while the gryphons are still bugged, or after taking the fixed gryphon to Arom's Stand, will avoid this.
This was my first time doing this quest, but it's apparently such a rampant bug that I'm surprised it hasn't been fixed yet...
Edit: To add further details, I was in Warmode, and as I recall there was no assault active in Drustvar at the time.