What I'm still not sure of us how 6cm, 2in makes this huge difference. I've heard of 5'11 people riding 168 boards and they don't have a problem.
As always, the tip to tip length of a deck means very little in choosing the correct board.
There are many factors that do affect correct sizing. Stiffness a big one. Each board size in a given model is designed and reinforced for a specific weight range. This is done using varied core thickneses, and laminates. That in combination with effective edge play a large role in determining what size is correct for a given weight range. Rider height has no impact on what size a rider should use whatsoever.
I hope that helps.