Eva is adorable! My daughter also had/has a H on her forehead/eyelid that grew to put pressure on her eye, actually it was very similar to Eva's. She developed severe astigmatism so we tried different things. My ped was the one pushing for surgery (unusual, I know) and I was very scared (she was 3 months old) so I pushed to see a ped derm who also gave me the option of surgery or trying steroids. We went the steroid route. Valentina was on them for 9 months. Her H responded very well and not only did it stop growing but also shrunk considerably. Unfortunately her vision did not improve (the hemangioma was sitting on her globe inside her eye cavity and putting pressure still) so we had no choice but to have surgery. She had a first surgery at 13 months old, which was a partial excision. Unfortunately the H grew back and the astigmatism got worse again, so she had a 2nd surgery with Dr. Waner at 15 months. This time all the deep H was removed and so far (4 months later) everything is well. I also consulted with several specialists via email. Its great that you are putting all your options on the table and making an informed decision. The GA comment is a really unfortunate one, probably just trying to scare you so you don't go ahead with something she doesn't agree with. I have also found that Drs sometimes don't respond well when you do your research and have a different opinion than them. They feel challenged and some might not handle that well. There is always risk of complications with GA, and although slim, that is one decision you will have to make.
Regarding insurance, my ins. did not cover Dr. Waner either but I requested an out-of-network authorization (or non-par referral) and after a few appeals got the referral. It is something you might want to try. I will be happy to share my requests and letters with you.
Good luck and let me know if I can help you in any way.
Marina, Valentinas mom
PS. I am attaching a pic before any treatment and a current one.