Stormanimagus and I collaborated on a GW version of the deck. I'm not playing the deck because I think the archetype's strength is predicated on temporary factors in the metagame. This version, however, has a lot going for it compared to the white version and should be a consideration for Eldrazi pilots.
History: I bombarded Noah (Storm) with UW versions with Reflector Mage, and he got back to me with a much better GW deck after the archetype did well in the P9 event. We did some tuning together.
4 Thought-Knot Seer 4 Reality Smasher 4 Thalia, Guardian of Thraben 4 Noble Hierarch 3 Eldrazi Displacer 2 Phyrexian Metamorph 1 Restoration Angel 1 Chalice of the Void 2 Stony Silence 4 Thorn of Amethyst 1 Trinisphere 4 Ancient Tomb 4 Cavern of Souls 4 Brushland 3 Eldrazi Temple 3 Wasteland 1 Strip Mine 3 Horizon Canopy 1 Black Lotus 1 Mana Crypt 1 Sol Ring 1 Lotus Petal 1 Mox Pearl 1 Mox Emerald 1 Mox Jet 1 Mox Sapphire SB: 4 Containment Priest SB: 3 Rest in Peace SB: 3 Nature's Claim SB: 1 Path to Exile SB: 1 Umezawa's Jitte SB: 1 Restoration Angel SB: 1 Stony Silence SB: 1 Aegis of the Gods
There are three major reasons to play GW over mono white.
#1 Noble Hierarch
Noble Hierarch is amazing in this deck. By improving the mana base, you get to play Stony Silence, which increases the value of Thorns and Thalias. You get to aggressively Wasteland. You get to more often cast the cards you want to cast on the turns you want to cast them.
The exalted triggers matter, as well, especially in the mirror. 5/5 Thought-Knots and 6/6 Reality Smashers are better than 4/4s and 5/5s. 4/4 Eldrazi Displacers or 3/2 Thalias can attack through a lot more opposing creatures than 3/3s and 2/1s.
Hierarch makes ever spell in the deck better and ever creature better once it gets on the battlefield.
Noble Hierach lets you skew your manabase heavier towards colored sources without compromising your explosiveness. This means you get to cast Reality Smasher and Rest in Peace.
#2 Stony Silence
Stony Silence is an incredibly important card to this archetype. Jason Jaco’s powerless version works because he plays maindeck Null Rods. These effects ensure your Thorns and Thalia’s do what they are supposed to do. They shut down Triskelion and Ravager and Jitte. Ravager MUD is a solidly unfavorable matchup for Mono White but even for GW. You can’t play Stony Silence or Null Rod in Mono White because the moxen are too important to the mana base. And you can’t use Eye of Ugin’s in White Eldrazi to solve that problem because you need to cast your white cards. Noble Hierarch lets you play Stony Silence and Thalia and Thought-Knot Seer in the same deck. Neither Mono White nor Colorless Eldrazi can play all of them.
#3 Horizon Canopy
This archetype has a lot of lands. Horizon Canopy is a great way to manage flooding. Noble Hierarch helps let us cycle it aggressively. Mono White should be playing Horizon Canopy over Plains anyway, so this doesn’t count as a reason to play GW over W, just to play GW over Wx.
An important note: going to two colors in this archetype is nearly free because the Shivan Reef cycle of painlands are better than basics and even duals. The Wasteland protection basic Plains theoretically provides actually doesn’t matter because Plains are your worst land and your opponent is never going to be wasting them over Temples, Tombs, or Caverns. Increased exposure to Wasteland in GW is alleviated again by Noble Hierarch, who actually makes this deck better against Wasteland than Mono White.
These three cards make GW better in the mirror, against Workshops, and against Combo.