When I want to show someone The Dear Hunter, I don't have a favorite song that I show them. I show them this, the purity and strength of his voice behind everything.
I've only been lucky enough to see the full band once - I was just utterly BLOWN AWAY by how on point Casey was. Every time I knew a big note or section was coming up I'd have my fingers crossed (god knows I've seen enough singers phone it in or just not quite pull off big moments) and he just fucking SMASHED every single one. What an incredible musician.
Every time I've seen them perform, they all give 100% consistently. The first time I saw them, like you, I was anticipating how these very difficult vocal sections would turn out live. But dude Casey goes for it every single time. I have a lot of respect for these guys.
Just Drop D. Otherwise pretty basic Major/Minor Chords for the most part with a few variations. Let me know if there is a particular part you are trying to work out.
Hopefully we viewing the same thing as the bridge. Tab wise, first chord is just 0-5-4-5 with the d a, d, and g strings respectively. Next chord is an F# Power chord, typically seen in drop d tunings, so 4-4-4-6. On the last time he slides the 4-4-4 to 7-7-7 and the last two chords are Bmin with some open notes and C#maj with open notes. Those chords look like this - Bmin - 9-9-9-7-0-0 and C#maj 11-11-11-10-0-0. All open notes are optional here. Sorry this isnt super clean but should give you what you need.