Well let me start off by saying we are no experts, but to us that looks like a prime candidate for laser.
It's sort of hard to see in our pictures because of where our daughter's superficial H was (the bright red part). Hers was more around the edge of her nostril and inside. But that bright red superficial H is exactly what laser is most effective at treating. That area did in fact turn black from the first treatment, and scabbed up within a few days, but then just sort of flaked off with nothing but new baby skin underneath. Actually that's not entirely true, it took two or three treatments before the superficial area was completely gone, but still.
Your picture appears to me as if your daughter's H is almost completely superficial. It may just be the picture though. Do you have any of the deeper purplish H?
Anyway, I understand being hesitant about this, but I would definitely recommend talking to a doctor that specializes in the pulsed dye laser treatment of these. Our Dr., Dr. Delfanian, I'm sure would be happy to speak with you. His contact info is available on this site, or e-mail us directly and we'll pass it along.
And lastly let me just say that despite seven laser treatments our daughter has zero scarring and I've never heard of anybody having scarring from these lasers.