If you want to make this strategy more safe .. just use 2 Darkmoon Zeppelin as back-up. They have Decoy, too - and they have Flyby, a flying attack. Granted, it is more weak than Alpha Strike, but it does work. Even though the last enemy pet is faster than the Zeps and can attack first. Even with reall bad crits - I haven´t lost this fight once withe these two as back-ups.
Just tried it again tonight, the Mechanical Axebeak died with the enemy's second pet still having at least 50% health. Next attempt fared better, with my pet getting the third enemy pet down to 317 health before dying.