I used a variant on the posted strategy, swapping Menagerie Custodian (1,1,2) and instead of Howl/Surge, I used Shock & Awe/Ion Cannon. I also use Darkmoon Tonk (1,1,2) as my 1st pet in case of emergency. So far I've been very successful with this strategy, I hope it helps!
Finally got it to work with Darkmoon Tonk (1,1,2), Iron Starlette (1,1,1), and Zandalari Anklerender (2,2,2).
Shock and Awe - get booted for Starlette
Wind Up, Supercharge, Wind Up
Wind Up, Wind Up (I think the Starlette died about here or got booted)
Black Claw, Hunting Party - then dies
Shock and Awe, Ion Cannon
anyway it was hard
I don't know how effective this is in reality, I only tried it once and it worked that one time but I might have just gotten lucky. Toothy wasn't fast enough, so I used Surge first, then after he got swapped out, I just made sure to keep Rip on Bucky, Blood in the Water off cooldown, and Surge if Rip didn't need to be refreshed. That way, swapping out just gave me my cooldowns back because the three are basically the same pet. Killed it with just Toothy alive with about 600 health left.