You still haven't proved, beyond the litmus tests, whether either Prime Spock or either Kirk are Gary Stu characters...
Okay...
Character S is one-of-a-kind human/alien hybrid.
He was made possible through a specific genetic project
He is the son of the high ambassador to Earth
He is from one of the most powerful noble familes of his planet
He has enchanced telepathic powers beyond anyone he works with, or anyone else on the ship.
He is smarter than anyone else on the ship.
He is stronger than anyone else on the ship.
He has a rare blood type.
He has female crewman fawning over him.
He has a troubled parental relationship which causes his exile from his home.
He is escaping an arranged marriage.
He has a rare and unique blood type.
He has all the benefits of being one race, and no weaknesses
He overcomes a racial limitation by force of will when no one else does
He is an expert in numerous sciences.
He knows several languages, and is fluent in all
He is immune to many things which harms everyone else on the ship
He is shown to have remarkable 'healing powers' that prevents serious harm from befalling him for long
He angsts about his mixed-breed heritage
He -is- a deux ex mechana on more than one occaision
He is a legend to his own people
He is a legend to the fleet
He constantly is praised for his abilities
He sacrifices himself many times
He dies, saving the main character and his ship
He is mourned by all of his peers
He is brought back from the dead
He outlives the main character
He becomes an important historical figure for later generations
He is revealed as a 'being of destiny'
How's that?