How old is the gas coming into the filters from the tanks? Is there any indication of water in it?
Have you checked the compression on all the cylinders? What was it and was it even from cylinder to cylinder?
Did all of the plugs you took out look the same?
Were any wet, carboned up or covered with oil, etc?
If you run the motor at night in the dark with the shroud off, can you see any evidence of shorting on the ignition wiring or plugs from observing blue flashes?
Did the carburetor clean-out involve a complete cleaning out of the jets, draining of the bowls, and replacement of any necessary gaskets? How about setting the float levels and adjusting the carburetor synchronization with vacuum gauges?
Does the missing occur only with the engine in gear (with a load on it), or in neutral as well at low and somewhat higher rpm?
I wonder if you could up a timing light on the motor and test to see if each plug is firing by moving the plug lead from plug to plug to see if the misfire can be seen as a non-flash in the sequence of flashes; e.g., when the misfire occurs, does the light not flash?
Have you run any carb cleaner and/or carbon cleaner through the engine, such as SeaFoam?
Do you have a Honda Shop Manual for your model? How difficult is it to check the engine timing?
Have you allowed the motor to warm up throughly to get any condensed water out of the electrical system, etc?
Many of our fellow C-Brast will also chime in on this, I'm sure!
Here's another source to ask:
Ask a Honda Mechanic
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Good Luck!
Maybe someone with a manual for your motor can suggest some more leads to follow up on...