One thing about it sputtering when you turn it off, its usually referred to as 'dieseling'. I learned here that the timing wont effect whether or not it diesels, because when you shut the key off no power will make it to the coil so therefore no spark at the plug.
Dieseling is caused by a buildup of carbon thats red hot and continues to fire the fuel when the ignition is turned off.
It'll take a little more information to figure out whats wrong. Dont know that the flywheel can effect anything youve described. If you pull the valve cover and turn the engine over you should be able to tell if you chipped teeth on the timing gears if the valves dont move properly.
I agree with what Dave says, if not a broken timing gear I would guess a problem exsists somewhere in the fuel system or ignition.
Jeff
