Well guys, making this post inspired me to double check myself, and I tried a little more.
On their own, setting ES_Framerate or ES_Frame to 0 do not accomplish this, but they do something...just not this. But together...forces united against evil....it bloody worked. I'm now able to stop the animation of "breathing."
I must say however, it's still relatively easy to notice a player in the same sense that it's easy to notice a func_illusionary.
Is there any way to change that? Make the player model less noticable? I've turned down the transparency a tad bit, but it still seems to change drastically with POV change (moving past it it's as if it updates every frame, whereas walls and landscape do not)