They also point out New Zealand had signed onto the International Maritime Organisation (IMO) protocol, which designates seafarers as essential workers.
However, this was not reflected in the Government's policies and seafarers are treated like anyone else. Meanwhile airline crews are exempt, for similar reasons.
Petursson, who is on a vessel off the coast of Argentina, said getting a space is "impossible" because the system is not designed for people working in their positions.
Petursson left New Zealand on November 19 last year, and said he would usually work two months before coming home for the same length of time.
Instead, he had made an agreement with his employer to work about six-and-a-half months because of the pandemic. He is working 12-hours per day, seven days a week.
"It's testing to do that for six months."
He has a visa to enter Argentina when his work-stint ends, where he will have to wait until he gets a spot in managed isolation.
Petursson's wife and children are in New Zealand and he thinks they'd like to see him spend less than seven months away.
"We're often in very, very poor internet connections ... we just can't see how we can possibly get those vouchers," he said.
Petursson said also having an Argentina visa put him in a privileged position, but was concerned about New Zealanders who could find themselves docking, and only given a 24-hour transit visa before being expected to fly home.
He had a colleague who arrived in Myanmar over the weekend, where a coup d'état began last week.
"His situation is quite frightening," he said. "As of four days ago ... he's still being told [by the Government] his situation does not meet the criteria for an exemption from the voucher system.
"I don't know what needs to happen to meet that criteria."
Schumacher's situation is different. The offshore geotechnical engineer is still in New Zealand and actually missed a job because of Australia recently halting quarantine-free travel from New Zealand.
"It was pretty much a blessing in disguise for me because I then would have been in the same situation," Schumacher said.
But if another job came up soon, he would likely go: "Because I've got a mortgage to pay."
Schumacher said he was speaking up for the people overseas. He'd set up an email account for stranded seafarers to contact him through, and in the past 24 hours about 50 Kiwis working overseas had been in touch about their struggles to book an MIQ spot.
"It shouldn't be part of their job that they know that if they leave for a two-month stint it's actually going to be six-to-eight months before they get home."
Schumacher said New Zealand could also be in breach of the Maritime Labour Convention (MLC) 2006, which allows unhindered repatriation of seafarers to their country of residence.
Maritime Union of New Zealand spokesman Victor Billot said they were working on a plan to help those finding it difficult to return to New Zealand.
They were meeting with the Government this week to discuss the issue and how they could assist seafarers get the best possible outcome.
A spokesman for MBIE, which controls the MIQ facilities, said seafarers whose overseas work contracts were ending and could not legally stay in the country of their final port of call could apply for an emergency allocation place on that basis.
These would be assessed on a "case-by-case" basis, they said.
If internet was poor, or for any other accessibility reason, the spokesman said bookings and applications for an emergency allocation could be made by a third party, such as by friends, family, an employer or other representative.
- additional reporting Michael Neilson
