It is possible to be under 6'3" and it is still an issue.
We had a BA student at PIK many moons ago who was very long legged, and would not fit into the Warrior. So the SE phase had to be conducted on the Bravo (AS202) much to the probably jealousy of the other students.
Your height ~ has it now peaked. Stopped growing?
Your present height should not be an issue on Boeing or Airbus.