How accurate is the story of Hiawatha and Great Peacemaker?

To start out with, there isn't a singular concerning the efforts of the Peacemaker, Hiawatha, and Jigonsaseh (the third major founder that is often neglected in these conversations). There are several different traditions, each with some slight variations. In particular, the Peacemaker's origins can vary. While he's commonly presented as having come from an Iroquoian group outside the Five Nations, other times he's from one of the five. Most founding narratives for the confederacy also contain a number of supernatural elements - from the Peacemaker's miraculous birth (which may be a post-colonial insertion into the story), or his preternatural stone canoe, or the violent sorcery of Tadodaho - which historians that favor a more naturalistic approach would view skeptically.

By and large though, the Peacemaker, Hiawatha, Jigonsaseh, and Tadodaho are accepted as historical figures and the broad strokes - at the very least - of the founding narrative is seen as legitimate.

What are some good books on the history of the Iroquois from a Native perspective?

I'd recommend The Rotinonshonni A Traditional Iroquoian History Through the Eyes of Teharonhia:wako and Sawiskera by Brian Rice and Iroquoian Women: The Gantowisas by Barbara Alice Mann. Rice is Nottoway - an Algonquian tribe that migrated north with the Tuscarora and were integrated into the Haudenosaunee back in the 1700s. He pulls from several different Iroquoian sources for his work, but Mohawk sources are of particular importance here. Mann is Wendat-Seneca, and Seneca sources get more time in the spotlight for her work. She also spends a considerable amount of time on Jigonsaseh's role in the founding.