More protection for Animar can include Clout of the Dominus, Alpha Authority and/or Aspect of Mongoose. They come out cheap and help a lot. Elgaud Shieldmate is another option if you want to keep more creatures.

I feel like with this deck's name Ulamog, the Infinite Gyre has to be auto included. Otherwise, it seems solid but I'm not an expert animar player by any means.

Elgaud Shieldmate is definitely more in the direction that I think I want to go with. I've also considered Lightning Greaves.

Oh, I've definitely a mind to add Ulamog, the Infinite Gyre and his brethren (sans Emrak) to the deck in the future. Hard casting eldrazi for free is what Animar is all about! At least, I like that noise. I also fancy the idea of adding Blightsteel Colossus or maybe the lesser Darksteel Colossus.