Rig Improvements
I originally modeled the head separately from the body. Today, I combined the head in Blender with the body. I also rigged the character again with Auto Rig Pro. This time the bones mapped more smoothly and worked well with the animations. The hands now grab when climbing and there is no separation of the head from the neck in any animation. I also cleaned up any seams in the textures that could be noticeable in Photoshop.
With Auto Rig Pro, here are the export Settings for Unity :