There is another way an American "Soldier" may seek refuge and that is through Contentious Objectors Status, an Army Regulation that may be applied through the Chain of Command. With this option available, it places Jack into an even weaker position.
"Conscientious Objection
The issue of the conscientious objector in a volunteer Army also received a great deal of publicity. Inevitably, some Regular Army and Army Reserve soldiers ordered to deploy decided to apply for conscientious objector status. The relatively small number of applicants was not surprising, considering that these soldiers had voluntarily entered the military. However, the small number of potential objectors showed that critics, who believed that many young people entered the military for educational benefits and did not intend to go to war, underestimated the sense of responsibility felt by these soldiers.
Active-duty and reserve soldiers who decided to apply for objector status were free to do so, but the Army
required them to deploy with their units while it considered their applications. Those who submitted applications were often assigned duties that provided a minimum practicable conflict with their asserted beliefs. Between August 1990 and April 1991 the Department of the Army Conscientious Objector Review Board reviewed 131 requests from soldiers in the Regular Army and 10 from the Army Reserve and Army National Guard. The board approved 89 of the above cases. Seven of the soldiers withdrew their requests.79
Several reservists and active-duty soldiers who declared themselves conscientious objectors received a great deal of press coverage. Spc. Stephanie Atkinson was the first reservist who refused to report, claiming objector status. Atkinson held that she had joined the Army Reserve for the educational benefits and claimed that she had never really considered."
http://www.army.mil/cmh-pg/books/www/www9.htm
If a Soldier truly believes they are in the wrong business, they need to find the moral courage and address it through their Chain of Command and not through a secondary country like Canada.