That's unexpected. I know someone who has small hands and I borrowed my phone quite some months ago to try typing and she types just fine. She can't overlap the fingers but she can reach the whole keyboard. Can it be that you can have a more pleasant typing experience just by holding it differently?
When I hold it, I place my index fingers on the exposed hinge, the phone rests between my index and middle fingers' bone in the palm of my hand. IIRC, that's also how she held it. How are you holding it?