Support, support, support...
He talks classical singing, but don't worry, the technique (appoggio) works generally.
He also talks about "single placement" -- which you can ignore, unless you want a classical timbre (chiaroscuro) that he mentions. chiaroscuro translates to "light-dark", and when used in singing refers to higher head tones (squillo) superimposed on lower timbral tones. It gives a classical sound, but a little of it can be used in contemporary singing. You may want to explore chiaroscuro a bit, anyway, because some of your voice seems to be leaning in that direction.
Really good tone you've got going -
I agree with above statements that more "support" is needed. You can find quotes of Eddie Vedder himself talking about that, somewhere. The intonation will improve with better support.
So while you continue to work on that concept, which is elusive for all of us, my practical advice is to feel it more. This is a tortured song, and although a "ballad", you'll notice that Vedder's energy level is still very high.
For instance , those crooning crescendos he does going into "and all I taught her was...." , that is an energy level very near to that of Even Flow and other PJ classics. Even the falsetto outro maintains a higher energy, as compared to, say, Brian Wilson's falsetto on a Beach Boys arrangement.
Sounds to me like you're sitting down singing? If so, get up. No sitting-down vocals for this genre. The support has to come from below. It's useful to think all the way down the feet even, into the ground, and you're wringing every last bit of energy out of yourself. This is very physical singing.
If you start straining and breaking in the mid-high range, ease up and let that support come up from below. It's harder to see in Eddie Vedder, because he's so physical, but the support is solid and you rarely hear him break or go hoarse unless he intended to .