Here is an older picture of her, you can just see the cut under her glasses on her left (our right)

So, today, with trepidation, I heated up a very small headed dental tool with a mild spoon shape on the stove and after washing Hazel's face, I smoothed the vinyl. I had read here about the spoon technique of repairing vinyl and thought it was worth a shot. I have to report that surgery was a success, and the scar is much less noticeable than before. Some small amount of vinyl ended up removed, and the remaining cut smoothed shut. We will see how it looks after some of Hazel's usual shenanigans, since she does seem to pick up dirt.
Here is a somewhat blurry after shot, but believe me, you would have been able to see it if it was still there.

She did get a nice wash first of course, and afterwards she recovered with a nice cup of tea in a MADh Vinyl mug. I was very happy that it came out so well. She is almost nine years old, and one of the original Haruka heads. This means that replacing her head with one of the same size is difficult! At that, her head is actually smaller than any other Haruka in the house! She is very special to me, and while the cut was bothering me, I really didn't want to make it worse.
So, if anyone has questions about more details, and what tool I used, just ask. Otherwise, join me in a great sigh of relief for a successful doll surgery!