Ms Coleman managed to reach the rescue boat, but her husband and three children, aged nine, seven and one; her sister-in-law and two-year-old nephew; her mother-in-law and father-in-law; and her husband's uncle all died on Thursday in the deadliest accident of its kind in almost two decades.
The Coast Guard said it will load the boat onto a trailer to hand it over to federal investigators.
The newspaper said that divers recovered a video recorder from the sunken duck boat that may provide clues to the accident.
The US Coast Guard said on Sunday it will oversee the salvage operations for the amphibious vessel that was carrying 31 people when it went down on Thursday in a fierce and sudden storm on Table Rock Lake outside of the tourist destination of Branson.
On July 19, the amphibious boat, modeled after World War II watercraft, capsized and sank in about 80 feet of water.
Tia Coleman, who lost her husband and three children aged one to nine, spoke to her aunt from her hospital bed and told her what happened.
A fire chaplain, Steve Martin, said that while most of the people who died were visitors, "they are not strangers to us". Once it was brought to the surface, the boat was drained, Coast Guard Capt. Scott Stoermer told reporters.
Williams worked for Ride the Ducks, the boat tour company which owned the vessel, but had previously worked as a pastor.
They also obtained video recorders from a second duck boat that had made it safely to shore and from the Showboat Branson Belle, which was docked nearby when the duck boat submerged.
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Live broadcast footage from KYTV showed a crane that is attached to a barge pulling the Ride the Ducks boat from Table Rock Lake on Monday morning.
Family of victims of the duck boat accident on Table Rock Lake leave after a community wide memorial service for the families, friends and victims at College of the Ozarks in Point Lookout, Mo., on Sunday, July 22, 2018. "Because they did alter the route of the boat".
Some witnesses have said the lake was calm and the storm came up suddenly.
Missouri law requires boat passengers ages 7 and younger to wear life jackets, but commercial vessels like the duck boats are exempt. The canopies on top of the vessels make it almost impossible to escape if they are tipped over.
Crews from multiple Missouri agencies are on the scene of a mass casualty incident with a "tourist-type boat involved", the Stone County Fire Department said in a statement. The National Highway Traffic Safety Administration determined that the front axle on the boat broke, causing the driver to lose control.
Suzanne Smagala with Ripley Entertainment, said the company is assisting authorities with the rescue effort and that the accident last week was the company's first in more than 40 years of operation in Branson. The investigation is being managed by the NTSB.
"In our family, my oldest son is autistic so a lot of things normal families do, we don't always do", she said.
"Thank you for your support, and we continue to ask that your thoughts and prayers be with the families during this hard time".
The NTSB, which makes non-binding safety recommendations, has urged the removal of canopies from the vehicles to reduce the risk of drowning.