I don't usually post on the forums, but you're mixing your inability to play the class on that fight with the class being unable to handle the fight. Obviously, you don't play brewmaster much, because you didn't consider chaining Purifying Brew as a cooldown, didn't mention BoB and ZenMed.
You don't need any cds for first grip, just use basic brews with BoB. You can Zen Med and Fort Brew the 2nd and 3rd grip. BoB is back for the 4th one. You can also use a trinket like Nightwell Residue if needed (which is not). I did pretty much that in +13 (with tyrannical) this week without any issues at all.