Nothing like a good thenewgreen response, inquisitive and open as ever.
Lacan is often criticised in philosophy (and was explicitly criticised by Jacques Derrida) as being too "phallogocentric". Phallogocentric means that you are developing knowledge from a "masculine" "linguistic" centric focus. This is why many deconstructionists would try to delegitimise Lacan's program by saying that his psychoanalysis basically amounts to a privileging of the phallic organ.
I tend to think this is a huge philosophical mistake. The first thing to note is that, towards the end of his career, Lacan specifically focused on the psychoanalysis of feminine jouissance (sexual enjoyment). For Lacan, as well as the many feminist Lacanian scholars who have further developed his concepts, feminine jouissance is perhaps the most mysterious and important of all psychoanalytic experiences. The second thing to note is that Lacan's paradigm (his "return to Freud") is meant to reinterpret all of the Freudian conceptual edifice (which relies on many biological metaphors) through the lens of structural linguistics. This means that when Lacan talks about the "phallic function" he is not referring to the "biological penis" but the way in which the symbolic is always-already overdetermining the "biological penis". I think this is nicely captured if one takes a close look at the symbolism of early human cultures where the phallus is always central and fundamental representation of ontology. Furthermore, in Lacanian psychoanalysis castration, basically the lack of "THE" penis ("THE" man) is something that all human subjects pass through (not just biological males). The consequence of castration, then, is that the lack of the penis (symbolic) is something which overdetermines gender identity for both men and women. For men they experience it as "not-having" and for women they experience it as "not-being". This negative effect is crucial to understand Lacanian metaphysics.
In terms of the penis as organ having an "outsized" emotional/mental impact, there is no question! But it is crucial to note that this "outsized" impact is something that must be read on the level of the symbolic and thus on the level of sublimation. It is not just the "sex act in itself" in which the "outsized" impact has consequences on the body. Indeed, for any human subject who "submits to the phallic function" and "becomes a man" (husband, father), there is a sense in which one is actually an "organ without body". The "phallic function" has "overdetermined" the body. This is the meaning of integrating the signifier "husband" or "father". It takes an enormous amount of integration of unconscious emotional energy to enact these roles.
I love your points about the strange way in which certain organs become important metaphors for feeling and action (e.g. penis, heart), whereas others would seem totally out of place (e.g. spleen). The heart in particular is an interesting metaphor, and I think it would be seen, or possible to interpret more on the level of the feminine jouissance.
In terms of animal emotions, I have recently been diving head first into learning more about the Wim Hoff method. I was really moved by his phenomenal description of learning the truth of the body and the brain imaging work that showed he was accessing the deeper emotional cores of the brain beneath abstract reason. For me, I am so in abstractions and so disconnected from my emotions that I have a lot of work to do to connect deeply with my emotional brain. From the descriptions of some of the neuroscientific literature on emotions, I would tend to think that emotions go down to the core of complex organisms. I think that emotions like "fear" and "hunger" are primal and core to their being. I think that the difference with emotions is that we have this layer of abstract self reflection and understanding. This layer of abstract self reflection and understanding filters the emotions and sometimes they can be "too much". Whatever is unique in humans, we may say from a religious point of view, is that this awareness of emotions is the core of suffering ("life is suffering"). It makes me think that the core difference between the sciences and the religions is related to the difference between the primordial scientific axiom of "I think therefore I am". With this axiom we have the pure abstract cogito (thinking subject) gaining an objective universal frame for being. What this pure abstract cogito sacrifices is embodiment (Cartesian dualism), and thus, perhaps, sets the stage for the division between science and religion. In the Western-Christian sense the body (and bodily resurrection) are central and primary. It may even be related to an axiom something like "I feel therefore I am" ("I love therefore I am"). This is totally foreign to the classical scientific understanding, but absolutely primary to the classical religious understanding. In any case, some of my thoughts. Not sure how I feel about it!