Try this for neutral..
Sail in neutral with engine off ,'draging' the propeller ,about 4 kts and up speed -not folding propeller, this one will stay closed. If the engine shake ( assuming cutless bearing and engine mounts OK and tight)you may have a slightly bent shaft!!If you have it out , check also if the unsuported lenght of shaft is not above the advise max lenght for that shaft diameter( there is a formula) , it might cause vibrations-and bent !.If you have premature cutless bearing failure ,check -along with prop condition and balance- if the lenght of shaft -from back end of cutless bearing to the end of shaft is not above 1.5-2 times it's diameter.Check if the engine is not mounted too high on it's bolts( there is an advised formula to that too ),this might cause excessive vibration , especially while heeling or rolling , and less if not...All this assuming other related variants to this problem were checked and found OK.Alternatelly ,if vibration change according to angle of heel , you might have problem with some engine mounts- or cutless bearing.These are just some options among others..Hope it helps. Alex.