He lost control of the boat while attempting to find a way out of a dead-end channel.
As he turned into another channel, one of the passengers heard him say, 'oh s***', and try to put the boat into reverse before crashing into the riverbank.
His partner, Ms Williams, said she remembered "ducking down and the boat suddenly stopping".
When she looked up she saw Mr Baker lying backwards with a branch, about 500mm in diameter, across his chest and with his seat in a recline position, the coroner's report said.
His seat was trapping a passenger, Leanne Lilly, behind him, who blacked out.
Ms Williams tried to reverse the boat back, activated a personal locator beacon and called emergency services. Others on the boat freed Ms Lily, but Mr Baker was unresponsive, with blood coming from his mouth, nose and ears.
It was not until two boats arrived to help that they were able to free Mr Baker, but he could not be resuscitated.
Forensic pathologist Dr Katherine White said the tree branch had crushed his chest, fracturing his ribs and preventing him from breathing. She gave the cause of death as traumatic asphyxia.
Coroner Devonport described Mr Baker's death as a "tragic accident".