Police believe Davey tricked Woodford into walking outside to her ambulance under the guise that his grandmother needed help before he attacked.
In a heartbreaking interview with Australian Story that aired in Australia on Monday night, Keith Woodford said he blames himself for not waking up the night his wife was snatched.
"I just want to know why I didn't wake up … why I didn't hear anything," he said. "And I'll always think it's my fault because I didn't do anything."
Woodford said he got home from work at around 8pm and had some food with his wife. He slept "right through until 6am" when he noticed Gayle was missing.
"At nine o'clock, I rang the clinic to speak to Gayle," he said. "They told me that she's not here and I said, 'Well, maybe she could be out at the airstrip'."
When he went there and she was nowhere to be found, he "knew something was wrong".
"I knew she was in trouble," he said.
An inquest into Woodford's murder found her killer had an extensive history of violent sexual offending and "slipped through the cracks" before he identified her as a target and carried out his twisted plot.
South Australian Supreme Court Justice Ann Vanstone told Davey his was a "cold-blooded killing of a woman who had worked with skill and compassion in your community" and he had chosen her because she was an "easy target, vulnerable because of her empathy".
After Davey was jailed for 32 years, Woodford told reporters he should never be set free.
"Dudley Davey should never ever be let out of jail for the shocking crime he committed. We will always mourn Gayle but so many people have helped us to cope with the tragedy of her death."
Woodford's family has made it their mission to ensure her death was not in vain. After years of campaigning for change, they helped bring about Gayle's Law – which protects health care professionals working in remote areas from attending after-hours emergency call-outs alone.