It is possible that the key is loose or sheared in the flywheel causing the timting to be off.
You should not need a larger main jet on the stock carb with a stock
Engine setup,go back to the #120.Unless there is modifications like pipe or adding much more air to the
motor ((
Internal Combustion Engine ? ))(twin intake setup).
I would not use either to start the machine ,especially since you have new rings and bore,use mixed fuel.
These machines are notoriuos for fuel bleed back and hard starting because it takes time for the fuel to recharge the carb and lines.
You may want to look into a
Goki starter for this motor (( Internal Combustion Engine ? )),for the buck it is one of the best options for it,and will keep the blood pressure from getting to high :) .
I wouldn't worry about an aftermarket carb unless the stock one will absolutey not work for you.
Was a leakdown test done after the rebuild ?
Are the floats adjusted correctly ?
Are the fuel lines installed correctly ?
Check all ground wires and make sure the motor (( Internal Combustion Engine ? )) is grounded to the frame from the case.