I would say I am very much in agreement with you, the "weakest link" so to speak is Erwin, in the sense that he had closed himself off the most with his plans within plans within plans, not necessarily maliciously but especially since there was always a certain amount of secrecy needed as well as they were dealing with elements within their midst, whether it was the enemy infiltrated within them or taking on the monarchy. A sad element to that is probably also the fact that the circle got smaller and smaller as this story progressed, I'm sure that he was very close with Mike for example, and the last piece, once again, the unreliable narrator of his self-recrimination and personal breakdown.
I would say that there was also a two way process here, that it was also because Levi was also constantly keeping an eye on him and picking up on the things that seemed off that created openings for the exchanges that allow? force? XD Erwin to erm, open up more to him as well XDD
Like you say, Hange's troubles had very little to do with their own self and a lot more to do with external circumstances blowing up around them. Their "shall we give up?" had more to do with a moment of weakness than debilitating self-doubt. They were also more easy-going, which would account for a lot, and ready to strike out on new relationships as well, Onyankopon, I'm sure that they worked closely with Armin as well, and even their ill-fated attempts with Pieck XDD, their eggs wouldn't have been as much all in one basket as Erwin I feel.
I agree that all three were close in their various combinations, but I feel like where Erwin and Hange would click best is when they put their criminal critical minds together XD I think that while Hange is better with making the initial interactions they tend to miss out on deeper undercurrents and subtle tells like Levi is attuned to (like Eren not feeling well for example). While picking up on such cues is Levi's forte and he knew Hange's tells as well, like you say, Hange simply didn't need as much help as Erwin. Erwin was a leader's leader to the detriment of his personal self, and only Levi got and I would also say persisted in getting close enough to be able to pierce through his bullshit as I like to call it XD
If we are allowed to believe that Name of Love is indeed "a love song to Erwin" as I like to put it :D, then I feel that they are thinking along the same lines as well, but just to point out a little special thing that I always enjoyed, while the last line 僕のこと 本当のこと boku no koto, hontou no koto is probably translated along the lines of some variation of "About me, about the real situation/truth", it can also be read as something like "About me, the real me" which is what I feel is like the secret bonus unlocked content!! :D and probably the thing that really marks out the special thing between them, that Levi was the one who got to learn the truth of Erwin.
Thank you for your ask! :)