Personally, I don't get the fuss about that line.
To me it's clearly: "bless each tear and the dirt I was born in, ruuuuuun"
It also fits the context for me: he's a fighter, struggling through hard times, but not giving up etc. It's the same old story we've heard over and over (lyrically). These are the kind of lyrics Jon craps out in 15 minutes and "bless each tear" is one of those typical cliché lines he writes (and that song is full of these).
He probably didn't think about it half as much as we did
I listened to it in the normal version, the chipmunk one on YT and the slowed down one that I posted that sample from. Sure, the hideous way of processing his vocals and the fact that he doesn't properly pronounce everything anymore doesn't help, but still it sounds quite clear to me. And I tend to say that my young ears (no offense to the older people here!!!) are usually quite good and spot on