Before I stated forging any wrapped eye axes, I purcahsed a couple lenghts of 1/2" x 1" stock and just focused on the eye. I formed and werapped/welded many eyes before I ever started on an axe. Do you have any info or phtots of the steps where you are wrapping, prep for your weld, etc?
I found that, for me anyway. having a clean sharp edge on both corners at the location of the weld, on the front of the eye, and a nice clean surface tends to help get both a cleaner looking and quality weld on the eye. I started clamping the "axe" in the post vice, while still flat, and using a hand fuller to really square up those edges before I wrap the steel.
Although I do things a bit differently now as far as the scarf cleanlines of the corners and location of fullers, here is a photo of the first axe that I did, pre weld, to get a bit of an idea -- if it helps any.