I know very similar if not identical decks have been posted, just showing definitive stats and light guide for anyone skeptical. I hit legend with this deck in August 2021 and September 2021. All stats are primarily D5-Legend. I do not have stats for this deck in other brackets as I was playing other decks.
*WARNING* If your current bracket is experiencing high volumes of pure aggro decks, do not play this deck. This deck excels against midrange and control decks which I experienced the most in D5-Legend.
Favorable matchups: any mages, any warlocks, any rogues, fel/quest demon hunter, quest paladin, non-aggro druids, quest hunter, quest/control priests
Neutral matchups : non-elemental shamans, shadow priest, deathrattle demonhunter
Unfavorable matchups: elemental shaman, handbuff paladin, aggro druid, face hunter
Do not keep - spells, Encumbered Pack Mule, or anything above 3 mana.
Always keep - 1 copy of 1-cost minions, Murgur Murgurgle, Sword of the Fallen, and Alliance Bannerman
Situationally keep - Hand of A'dal if you already have a 1-cost minion. Northwatch Commander if you already have Sword of the Fallen. Oh My Yogg! if you are going first and you want to risk trying to burn an enemy Questline; while it is amusing when it works, this is not recommended as any opponent paying attention will coin first to not risk it.
Here are my mulligan stats. While Varian, King of Stormwind has had some clutch moments for me, it was statistically the most underperforming card either just sitting in my hand because I would end games before turn 8, or played in desperation barely getting a 50% win rate when played. If you've made it to turn 8 and can't foresee lethal by 10, Varian will just feel clunky and expensive. Solid alternate options include Moonfang, Ogremancer or Overlord Runthak.
When playing unfavorable matchups all you can really do is try to out aggro them and hope for god draws. Clear minions with weapons, and for aggro druid specifically try to keep their board completely clear before they spam buffs.
All other matchups, turns 1 through 5 focus on maintaining at least two of your minions on board. Chip their hero every turn if you can, but minion trades will be necessary to ensure you keep two on board. Liberally play Hand of A'dal to do early hero damage. Play Northwatch Commander after attacking with Sword of the Fallen whenever possible. Try your best to maintain 2 minions on the board, and if possible get Cariel Roame reductions on Conviction (Rank 1)
Turns 6+ you should be able to do lethal with some combination of your remaining minions, Conviction (Rank 1), and Battleground Battlemaster. If you aren't quite at lethal, consider playing these cards anyway if you can get lethal in 2 turns, but only if you can maintain board control. Otherwise keep chipping and maintaining board until you can lethal with Conviction and/or Battlemaster.
Here is the win/loss spread for September 2021.
Legend shot from today: