It's not bad, but there's so much unrealized potential.

Just from Sartre and Heidegger and Kierkegaard there's more that could be explored. You mention Schopenhaur, but you could even take it a step further with Nietzsche!

Sartre's Bad faith: Shinji chooses not to act because he's afraid of the responsibility of freedom, but denies his refusal to act by claiming he's powerless. Asuka gets Shinji to 'act out' a kiss because she has some level of emotional attachment or attraction she doesn't want to address. Misato realizes the cruelty of forcing children to go through war and her role in it, as well the acknowledgement that she could refuse to force the children, but rejects the responsibility by claiming she's following orders and then attempting to act like a parent. Gendo attempting to bring about Instrumentality is a way for him to avoid the responsibility and knowledge that he is still a being capable of love, and what he 'owes' Shinji as a father.

Sartre's Gaze: So much of this show involves Gaze, the fear that comes from being objectified by another and having the totality of your existence reduced to a single facet as well as people using Gaze to promote images of themselves. Asuka has basically spent her entire life trying to use Gaze to convince everyone (including herself) that she's an excellent pilot and thus deserving of love. Rei, primarily in Rebuild, concerns herself with trying to 'appear' and thus be human like others by attempting to mimic the proper affect. Shinji has spent his whole dang life being subject to the Gaze of others, especially Gendo and Asuka in multiple situations where his humanity has been reduced to his ability/willingness to pilot an EVA.

Heidegger's Anxiety and Dasein: "A human being is an existence that is aware of its own awareness," is a simplified example of how he describes Dasein - a Being that is capable of contemplating its own existence with the ability to shape that existence with the knowledge it will one day end. Dasein is a being that can experience Anxiety, the temporary disruption of everyday existence in the Fallen word in which an individual must choose how to live their life and create meaning in the face of the knowledge they will one day die. And they must choose whether to become Authentic by creating their own set of values or return to Fallenness by letting themselves be absorbed by (in Shinji and Gendo's case, music as well as) everyday living.

Shinji and Gendo (as revealed in the Rebuilds) are both individuals who experience frequent bouts of Anxiety, but in their youth they reject Authenticity and Fall into just doing everyday tasks without care and isolating themselves because that's easier than being Authentic. Shinji's attempts to be Authentic, to choose for himself what he desires and how to live his life are what lead to his departure from NERV (after he tries to destroy it) and the (partially realized) Third Impact of the Rebuilds - and eventually the decision to remake the world.

Kierkegaard's Either/Or: There's a whole section in Either/Or about how choice is required of living beings, how personality can be crafted from choice or subsumed when the individual refuses to choose out of the belief that regret is inevitable. In addition, the section includes how an individual who rejects choice while living attempts to delude themselves into thinking both options remain available, but in so doing only makes himself miserable. This is Shinji (and Gendo when he was younger). He rejected the act of choosing for himself because he doesn't really have goals or desires, because he's not Authentic, and in so doing ends up in a lot of bad scenarios or ends up acting impulsively and seemingly without reason because he thinks his actions will always end in regret.

Nietzsche: There's so much potential here, the aphorism about how being loved can be disgusting or unsettling because the person being loved is full of self-loathing (Shinji, Gendo); because they see themselves as unlovable. The idea that every philosophy (and anime) is an attempt for the author to justify their own existence and that 'all writing is done in [the] blood [of the writer]', (Anno's 'journey' through depression). The idea that being known by another, and their attempt to understand is painful because understanding and empathy are their own forms of suffering (the hedgehog's dilemma and why Gendo/Shinji/Asuka/Misato put up so many emotional barriers).

The entire dang series could be seen as a promise/threat of Eternal Recurrence and the problem of Nihilism. Shinji and Gendo have built their lives on a basis of fear and rejection of life, a desire to never do any of it again, a rejection of pain and in its essence life itself - they become Nihilistic in a negative sense seeking only the end. Kaworu accepts the pain because of the love and joy it enables, he accepts life, and has literally lived his life repeatedly without end (until 3.0+1.0) in pursuit of helping Shinji learn how to do the same - Kaworu recognizes that while there is no definite objective meaning in the universe, meaning can still exist and creates/seeks his own. It is only in 3.0+1.0 after Shinji learns how to accept his life, to accept life and wish to do it all over again, to will the Eternal Recurrence, that he becomes able to literally break into a new reality. And the idea that acts can exist beyond good and evil (especially when they come from 'love') comes up repeatedly, it's why Shinji tries to save Rei and causes the partial Third Impact, it's the idea behind Gendo's pursuit of Instrumentality, it's why Kaworu spends who knows how many lifetimes trying to save Shinji.

Even after all of this, there's still stuff - just in the authors presented here - that could be further explored.