I updated the initial post with a few different items discovered using lootzor, I took out Elixir of Mastery as it wouldn't stack with the Elixir of Major Agility (it still gives more avoidance than the flask), I added in the Scroll of Agility V, and I discovered that I DID include the enchant "Enchant Weapon - Greater Agility" in my inital post, but forgot or something. Stats from the enchants stay the same.
I am now at 3.64% chance to be hit (blocked hit, of course). DW isn't the best option as the shield listed offers better avoidance than any weapon, even if that weapon has another +20 agi enchant on it. Also, as Malazaar mentioned above, without a shield you turn 3.64% chance to block into 3.64% chance to be crushed.
Note that if I put mongoose on the main hand instead of the 20 agility, 100% immunity will be reached every time mongoose procs.
Forgive me if I missed this but are these statistics for a level 73? The avoidance shown on your profile is higher than the avoidance you have against bosses. Did you include that into the calculation? Forgive me if you did, I just didn't notice it.
Generating threat might be easier than you think, since you can pretty much tank with only 5 points in protection and even in Berserker Stance :>
Then you'd be a naked DPS warrior with one weapon. A Prot warrior would probably do more damage in the same gear, and beserker stance is terrible for generating threat -- 10% more damage and 3% crit do not come close to making up for -36% threat (compared to talented defensive stance).
As someone mentioned theres definate application for it for a couple of fights. Not like you need it but Al'ar phase 1 would be another example where a 100% avoidance tank could keep aggro indefinately without being hit. Pretty pointless but fun!