Etanercept is conventionally used to treat severe arthritis but American doctor Edward Tobinick injects it into the base of the neck of brain-injured patients to reverse injury. It is said to have been effective in hundreds of cases.
The US$6000 ($6900) treatment has brought the Elliotts hope for the first time in almost a decade.
"We're trying to protect ourselves with not getting too excited but it's hard not to get excited and not let your mind wander," Mrs Elliott said.
"To be able to talk to the kids for Luke would just be massive. He's never really been able to tell them how much he loves them properly."
Mr Elliott was 24 when he suffered the unexplained stroke. Mrs Elliott, a schoolteacher, said her husband was in Middlemore Hospital for months learning to walk and talk again. He can say some words, but his speech is not consistent. He walks with a limp and can't use his right hand.
The part-time teacher aide does most of the child-rearing because Mrs Elliott must work full-time to support the family, but she said her husband has found ways to change a nappy and even tie a balloon one-handed.
Mrs Elliott said they were aware of the criticism surrounding the unorthodox treatment, because it had not been through a medical trial, but said her husband had nothing to lose.
"We can't live the rest of our lives thinking why didn't we try it?"
The family has raised $11,000 toward the cost of the December appointment at the Institute of Neurological Recovery in Los Angeles.
However, neurologist and stroke specialist Professor Alan Barber of the University of Auckland said there was no evidence that Etanercept had any effect in people who had suffered a stroke.
"The programme in North America is expensive and people should consider very carefully whether this is a good use of their money," he said.
Stroke Foundation of New Zealand chief executive Mark Vivian had heard about Etanercept but did not know of any evidence of its efficacy.
Luke Elliott's Givealittle campaign can be found here.
Etanercept
• An anti-inflammatory drug that blocks small proteins in the brain known as tumour necrosis factor (TNF), which cause cell death
• The drug has been used on Alzheimer's patients and is conventionally used to treat severe rheumatoid arthritis
• It is injected into veins at the base of the neck
• Patients are tipped upside down to let the medicine flow to the brain, where it is said to reverse the effects of stroke and traumatic brain injuries.