Aaaah while you are all somewhat correct you need to look at the problem from a different view.
You have a resonant vibration issue. There are lots of vibrations happening in the boat, some are small, so much that you cannot even feel them...... What you need to do is change the resonant frequency, your prop etc may all be in tolerance, but the combination of all or some may combine at a particular frequency.
So, what to do, change the frequency, you can do this and you do do this when you throttle the engine. What you need to do is change the frequency at which the mirror resonates......remove the mirror glass from the housing and glue or attach a lead weight to one corner, maybe try two corners and use say fishing sinkers, get reasonably large ones that you can hide in the housing, do some experiments, I think you will find some success, try it.
This is a common fix on car mirrors that may suffer the same sort of vibration issue.