The case against Ross, a former Black Watch soldier decorated for outstanding service in Iraq, was brought to court after police carried out a cold-case review in 2007.
He was ordered to spend at least 25 years behind bars following a trial at the High Court in Glasgow and later handed a further five-year sentence for trying to flee the building after the verdict and stashing weapons in a car.
Prosecutors claimed that Ross's racist views drove him to hunt down and murder one of the island's few Asian residents. The Court of Criminal Appeal in Edinburgh upheld his conviction in April.
His legal team had argued that police interviews, conducted without a lawyer present when Ross was 15 and 16, were "unfair" and the trial judge "erred" by refusing to allow the defence to lead evidence from a psychologist.
Ross was refused permission to take his appeal against his conviction to the Supreme Court in May.