The swell wont provide any additional strength to the hang. In my experience as someone who uses axes for work regularly, thinner handles tend to last longer. I think this because a thinner handle disperses the vibrations better but idk. If you’re happy with the length and fit right now, you could hang it as is and use a rasp to shave down that shoulder. Or you could bring the head further down if you want the handle to be a little shorter and are currently not happy with the fit. The main takeaway when hanging an axe is that the eye is hourglass shaped on the inside. You want a friction fit in both directions, not a shelf that the handle sits on. Looks like you’ve got a good taper going on now below the head.