These are not value-neutral. To identify with or to experience does not equal perceiving in the sense that you need for your argument. And this is not by accident — empathy has a moral component in that it places the point of view of the other on a level with your own. There simply is no identification with or experiencing of anothers position without also accepting it as valid.
So no, I’m not trying to redefine it. You, on the other hand, are trying to remove fundamental aspects of empathy.
And I take it that you will not agree with this. I cannot convince you that your notion of empathy is faulty, and you will not convince me either.
One last note: for someone intent on pointing out condescendence in others you don’t seem very unhappy about being condescending yourself.