I actually might have found a solution. I was just experimenting.
I’ll give exact details on what I did, but for now, animating the armature in the pose mode will keep the origin in the same place it was in object mode, but when you animate the armature in object mode, the origin should move with the armature.
What I did was I animated a walk in place action in pose mode; then I animated the movement action in object mode (both animations were done on the armature). Animating in object mode ensures that the origin stays with the armature. It might feel ridiculous at first because with the animation in object mode, all of the bones are static, and moving as a whole, but in the end it worked.
Next, this is what I did with the logic bricks
I put in a boolean property and named it near. Basically, I played both the walk-in-place animation and the movement animation at the same time. NOTE: in my experimenting, I found that it is important that your walk-in-place action and your movement action both have the same start/end key-frame numbers (My walk animation was only 25 key-frames while my movement was 100, so I had to duplicate the walk animation 4 times so that it could end at 100 key-frames.)
Then, whenever you trigger the boolean to be true (You can do whatever you want to trigger it.) the mouse will immediately start seeking the human (also notice that I had it playing the walk animation, even while it was seeking the “human”).
I really hope that helps!! I you have any questions, please ask them; there might be a delay in my response though.