I'm assuming by "smooth part" you mean the ring that in the middle of the nurling and not the smooth part in the middle.
If your more stable overhead with your current grip then just be more patient with the pull. If you're being as patient as you can be and your still hitting the thighs then I would move the grip out. There are ways you can strengthen the overhead position in the Snatch.
I suggest posting a video of you snatching for a better analysis.