Re: engine question
It would also be useful to know what kind of a boat the motor is mounted on. The type of boat, length, approximate operating weight, etc. might provide clues as to the problem. If the boat has a tach on it, you should also state what rpm the motor shows at wide open throttle (WOT).
Absent any indication of mechanical problems, this sounds very much like a boat that is underpowered, or an engine that is overpropped. The initial "bogging down" and/or vibration, followed by a more normal operation of the motor, sounds like a boat trying to push through its bow wave on accelleration. The eventual transition to a "normal" sounding and performing engine, could just be that the boat has come up on plane. If this assumption is correct, the WOT rpm value will probably be at the lower end of the manufacturers recommended range, and might even be below it.