I'm guessing a little, but I'm pretty sure that is either the fuzz face, big muff, or sub octave fuzz model from the Line 6 Distortion pro. The M13 has those sounds in it as well. I'm not sure how you arrived at the fuzz gun pedal, but I doubt that is what the Edge is using here.
I've had a hard time getting some of those drive tones from the Axe-FX, not because they aren't in there, but because they take a while to find. If you get frustrated trying to get the drive tones just right, I suggest you pick up a DM4 or an M13. Those sounds are literally all over the latest U2 albums, and you can dial them in very quickly on the M13 as opposed to the time it takes to get them right in the Axe-FX.
In the AFX, I think you're right on track with the hard fuzz. The first thing I would try for that tone is to use Javajunkie's fuzz face settings that are somewhere on this board (maybe in the wiki), and then lower the bias some. That would be my starting point to get this sound. If that isn't it, I would try lowering the bias some on the Big Muff model as a starting point. If it's the sub octave fuzz he's using, you'll need to try some combination of the drive block and the octave divider.
I can't tell for sure if it's the sub octave or not. It doesn't have much of the lower octave mixed in if it is, but that model does have the ragged, raspy, and huge character of what I hear in the video. I like this tone a lot, so I may try to dial in something close if I have some time today.
He's playing a hollowbody with P90s too, so that's a big factor in the sound he's getting.
D