I agree quite a bit with what you've written here, Mallz. So long as we understand that His hatred and mercy are not two different parts of him, such that when we are unrighteous we relate to Him through this part called wrath and when we are hurting we relate to Him through this part called mercy, then you've stated it very well. To the extent that we speak of divine emotions, we are (like when we're discussing divine attributes) talking about the way that our intellect conceives of this selfsame essence. We are the variable, not Him. It's just that in the case of emotions, our language is analogous twice over. That is, in the case of the normal attributes, we are speaking analogously by one step. So God has power, but because He is identical with His essence and existence, the way in which we think about His power is only similar to how we think of our own. Or put differently, we identify in ourselves this thing called power, and we see that God can be thought of in some very real sense of having power. That's one way to consider the divine essence. Since we are finite, we cannot consider it, in itself, fully and completely, so we have to think about it within one particular mode, and that mode must be from our own perspective. And since our perspective is that of a composite, temporal entity, so we think of God that way. And so while there truly is something "like" power in God, that "likeness" makes our language analogical.
But in the case of emotions, we have a double analogy. So let's take sadness. When you feel sadness (or any other emotion), you have an intellectual judgment of a particular thing and then a physical reaction to that judgment. So a thing judged one way with this particular physical reaction, we call sadness. Now, in God, we have judgments of things (by analogy, of course). But we also have this analogy of an analogy in the idea of a physical reaction. God obviously doesn't have a physical reaction since He isn't physical. Nor does God react. But insofar as the physical reaction is closely related to the nature of the judgment ("that is sad!" we say), there is a sense in which we can see a similar type of "reaction" in God. So that's why I say such language is a double analogy: an analogy of an analogy.
Anyway, as to your question, I say that simply because John wasn't trying to write a metaphysical thesis. If you had asked John if he identified this emotion called love with God Himself, He would be confused by that. He would talk about how important love is and how it trumps all things. But even then he'd be less interested in the emotion per se and what it is rooted in . . . the idea of putting someone else's needs before your own, of doing what is good for them first, and so on. The "others orientedness" of love is what he would focus on, not the physical reaction in your body we experience as "love." John understood clearly that God doesn't have a body. He says that God is Spirit, and spirits don't have physical reactions to anything and so don't feel "love" in precisely the same sense we do. They don't feel anything sense feeling is something that bodies do! So they "love" in a sense similar to the way we do but not identical to the way we do. And that's enough to show that "God is love" is analogical. It is true as stated, but it's true in an analogical sense.
I agree His hatred and mercy are not parts of Him, they're of Him. But I think we as His image we're created to explore and express Him towards everything for eternity. We will never know Him, but we will always try (remind you of marriage?)
I think that when we are unrighteous and know it we can feel shame which would only exist against a God and we can relate to His nature through this shame but we know it doesn't end there, nor is it an aspect of Him, but of us. And I see feelings are generated from the spirit, and the body and its interactions are the processions. I don't view feelings as merely chemical reactions and actually view the current state of our body feeling emotions (expressed physically) to be restrictive of what would otherwise be truly expressed by the spirit (which could go into the aspects of a glorified body and why humans never had one to begin with). Humanity is an evolutionary stage for us and to God
So, I agree with what you say, but think that we do relate to Him when we are under His wrath, knowingly or not and not only feel the state we put ourselves in physically, but spiritually and towards everything around us.
About the relation of power. I know we can't consider it fully as we will not ever know it fully. But I think the procession of power can be fully known through everything processed from God. And though we are currently finite, we know we are currently not through Christ as being adopted as children of God. I just can't help but have a problem with the term analogy (or analogy of an analogy). Take the instance of John talking about love. I see his words as spirit. I see him when talking about love to not only be talking about the feeling, but the essence of the feeling. We can relate through our feelings but we know love is more than feelings (agape, as you were elaborating on above); I propose the genesis is spiritual and the physical is a procession (this is even more of a hypothesis). So, I see that I mirrored a lot of what you said and we pretty much agree on most points. But I disagree that feelings and emotions are purely physical (even in carnal relation in our state towards Him); they are processions of the spiritual and are dumbed-down and a diminished expression of the spirit.