Actually he has all the legendaries he needs for a control Warrior deck, Ragnaros, Ysera, etc are all completely unnecessary. Also, yes, he does actually rely on drawing Alexstrasza and Grommash, the whole point of Warrior control is to stall until you get them, even if it requires you to go through all 30 of your cards, it's more than capable of doing so with all the removal options available and of course the armor.
So OP, I'd definitely add the Cruel Taskmasters, they're extremely versatile, pinging off 1 health minions, pinging a minion to Execute it and most importantly using it on Grommash for the killing blow. Inner Rage has the same effect of Cruel Taskmaster, just without the body which isn't that significant and costing 0 mana to compensate, so that's the 2nd card I'd include. That leaves 2 cards left or 1 card slot left. From your list I'd either include the Arathi Weaponsmiths or Harvest Golems, leaning more towards the Weaponsmiths. If/when you get access to more epics and legendaries I'd bring Baron Geddon(he's excellent at stalling) and either Big Game Hunter or Black Knight, probably remove the Auctioneers for them as you aren't really spamming your spells, use weapons for a lot of your removal and Auctioneer usually doesn't live for more than a turn, 2 max, so you won't get as much usage out of him as in more dedicated decks like Miracle Rogue, Violet Paw Druid, etc.