Actually I forgot to mention that something else we have discussed as a middle name is
Evelann. So.. Hannah Evelann
With that name we are incorporating my grandmother also not just his. Her name was Evelyn. I'm not 100 sold on it but I think it's cute and different and I definitely like it!
What about Hannah Lyn(n) Ann? Then you're incorporanting the "lyn" from Evelyn and keeping Ann.
I appreciate what you're trying to do with Evelann, but it's a pretty bad smoosh name.
Good luck deciding. Naming a person is hard!