Getting in here late... read all of the above. It seems strange that the engine would be running fine, then as throttle was given to get back up on plane.... shaking and misfiring came into play. However, regardless of whatever problem the engine's encountered, the thing to do is start with the basic trouble shooting procedure.
What comes to mind due to the shaking mention is a powerpack diode failing, causing two cylinders to fire at the same time... BUT... do the following first.
Compression... All spark plugs removed to obtain the highest cranking speed available. What are the psi readings of "all" the individual cylinders?
Spark... Spark plugs (all) still removed. The spark should jump a 7/16" gap with a strong blue lightning like flame... a real SNAP! Does it?
Piston Play... A/Plugs still "all" removed. With a large screwdriver, or tool of your choosing, let it lay gently on top of a piston. Crank the flywheel by hand to TDC, then continue cranking the flywheel slightly, dragging the piston down a inch or so. Now, gripping the flywheel so that it cannot move, shove down on that large screwdriver... the piston should not be able to move without trying to cause the flywheel to move.
Let us know what you find.