Oh, this looks good! I actually don't think the eyes are totally the issue here; I think the one that's further away may just be a little squished (I do this a lot myself). Eyes in 3/4 views like this are usually about the same height as each other, with the one further away being narrower (if that makes sense; I'm on mobile but can't find the simple guide I'm thinking of).
I looked at the artists you mentioned and I see the issue here, but I think you're close - you're drawing these features fairly realistically (and good job! That nose is seriously impressive), while, like you said, both of them are more stylized.
Peacchip's eyes in particular have very clear shapes to them (does that make sense), and I think both draw them a bit larger. In both cases, the rest of the face plays a role, too! Both of them draw simpler noses and mouths, and I think have more dramatic line weight differences (thicker upper eyelash, thinner lower eyelash, a more "anime" shape, less detailed folds). I also think pushing the eyebrows and mouth will help achieve the expression you want. You know the rules, but you aren't quite breaking them yet.
I don't think you have to do much to get where you want here - you're really close! Good luck! I'd also suggest checking out some Satoshi Kon movies for another style that's fairly close.
Edit: Sorry for bringing up stylization, I'm a bit sleep deprived and missed that you had already mentioned that.