Some people opt to try Hagara (25H) before Yor'sahj since it's mostly just execution.
Now that you mention your cooldown options, what's your healing composition like?
It seems that ~36k/player (250k raid) is the typical DPS that most groups kill Ultraxion with, though there are some rare parses with raid DPS as low as 230k (~33k/player). I would hate to do it with the bare minimum though, as the last minute of the fight is really shaky to heal.
That is quite a frustrating thing to experience, and I think I know it too well. :/