Do you hear a rattle in neutral when in the water?
Does the noise occur in reverse at idle?
Does the rattle noise stop if you increase the in gear rpm slightly?
Have you checked your gearcase oil for metal shavings?
Does it make the noise at all in neutral?
You have to think about the bearing layout in these gearcases. The driveshaft is ALWAYS spinning, so if when out of gear you do NOT get rattling, you can probably rule out driveshaft bearings as well as any crank bearings in the motor.
My guess would be you have a bad bearing or gearset on the propshaft.
A different prop may make the difference as it is probably just the "unloaded" gears and clutch dog moving within the normal free-play. This is very true if a blade is not exactly equal to the others. As the revs increase slightly, the load increases enough to keep the gear teeth and clutch dog lugs tightly engaged.
Other makes and models of outboard motors can experience similar symptoms due to the exact same reason of free-play clearance that has to be designed into gears.
There is a possibility that the shift cable was not adjusted properly on installation and that can be easily checked by your dealer.
What is your top full-throttle rpm with a normal load on board and what kind and size of boat?