Earlier, I tried editing the root transforms of my MoCap rigs in Blender. It failed miserably, the animations broke upon import into Unity.
To fix the issue where the character rig was moving around inside of the character controller, and not staying centered in the view, I had to un-check apply root motion in the inspector. I will re-check it once I have all animations completely zeroed out at the origin.
To create my states and blend trees so far, I used a combination of animations from Mixamo, Crysis, the Unity Asset Store, and my own motion capture. Any animations that had to be purchased, I did so months ago and they have been sitting on my computer, unused--until now. As you can see, the locomotion and camera issues from last week have been fixed. The character no longer moves around off-center with the camera. I used Unity IK to bind the left hand to the rifle. The character can run and sprint in all directions as well as aim and strafe when the player presses the left mouse button. The aiming is off-center, but that will be resolved once I setup aiming controls.