I sat before Tamer Vesharr for a few hours this morning trying to find the perfect ELEKK PLUSHIE-WORTHY team to beat him. I was looking for a team that could hit his back-line and kill the third pet so I wouldn't have to deal with it's heal.
I went through numerous teams of my own, and several strats. from other people, and I finally found one in the wowhead comments, by Sybreedx. http://www.wowhead.com/npc=87123#comments
His Chrominius + Pandaren Dragonling team allowed me to get in a carry pet without having to make any moves with it, or get hit.
I tried your strategy first, and I tried it several times—and thank you for going through all the trouble to record and post the video... But I tried doing it exactly the way you suggested, and then when that didn't work I tried changing up the hit order. Maybe with some RNG luck you can do it; but not without a lot of hair pulling.
I hope someone will come out with a solid Plushie list soon that can be stickied. Sybreedx's team should definitely be on there. Please vote him up so it can go to the top of the list (and vote the other comments down).
I'm making my own list of Plushie-worthy teams that have low failure rates. We need a stickied list!