I re read your post Jeremy.
I see the problem. Don't try to bend it around the drift. Just bend the whole thing over the edge of the anvil. This requires a welding heat too. Naturally the thinner eye walls will be where the bend takes place, right where it thickens at the poll. That's ok for now. You are just getting everything lined up and prepared to grip it by the front "lips". Once you figure out how to hold it, put it back into the fire or forge and get the poll very hot. Bring it out and drive the poll sides in flipping it to keep it even. Flip it with your wrist, not by sitting it down and re gripping. You will lose too much heat that way. While doing this, don't crush the walls in closed. They will get distorted some but that is what the drift is for. After the weld you can re shape the eye with the drift.
Also in your post you said you were trying to weld a poll on a hawk. I don't put a poll on a hawk. Not sure if you made a typo.
Look at these three pics and see the stages. This is an axe.
Folded. Notice that the eye walls are bent and not the poll. This just right for the moment. After you get a grip on the front end, you re heat and drive the poll sides inward as I mentioned.
This is after the poll has been driven in on the sides but before the weld. Same axe.
After the weld the eye is drifted to shape.