Sgt Paul Meyer took the Hercules C-130E transporter from Mildenhall, Suffolk, in a bid to fly home to his wife Jane in Virginia in May 1969.
It disappeared from radar in the middle of the English Channel, as Sgt Meyer flew it after a night of drinking.
The Deeper Dorset group is to use sonar gear to search for the crash site.
The official record of the crash recounted how after the heavy drinking session, Sgt Meyer, 23, escaped police custody, impersonated a captain and ordered the Hercules to be re-fuelled before taking to the skies.
It described his action as a "highly irrational act" and said he was "under considerable emotional stress".
The mechanic who had previously served in Vietnam, had been refused leave shortly beforehand.
His stepson Henry, who was seven at the time of the crash, said he remembered Sgt Meyer as a "genuinely good young man".
He said he had been keen to return home to help Henry's mother in a custody battle.
"Paul was a patriot and loved his country - it seems he just loved his family more," he said.
"This may or may not find an answer to what happened, but we are so gratified and it'll give our family some closure. It means so much that people haven't forgotten Paul."
Simon Brown, of Deeper Dorset, said the group had studied official records, as well as tidal movements and weather conditions to identify the crash site.
He said they had "five good targets" within 10 square miles of seabed mid-channel, about 30 miles off Portland Bill.
Mr Brown admitted finding definitive proof of what happened to Sgt Meyer would be "very, very difficult".
"He did a fantastic job to get a complex plane off the runway - to fly solo is quite an amazing feat.
"Whether he flew into cloud and got disorientated, or was shot down, we're not discounting anything."
The group has launched a crowdfunding appeal for £6,000 and aims to start sonar scans of the seabed later in the year.