I've also heard 50 percent distilled white vinegar with 50 percent distilled water works good to clean a carby in a Ultrasonic cleaner.
Yes it's a good idea to try a new carby to see if the problem is the carby. Sometimes I clean and check and adjust a carby so I think there can't be a carby problem then when the motor is still running rough I bolt the cleaned carby to a motor I know doesn't have a problem and the carby works fine , this saves time then you don't spend any more time on the carby.
As we know the Honda has a pilot screw adjuster and a pilot jet that needs checking / cleaning.1 and 2 in the pic below just need to pull the screw out above the pilot jet to clean the jet.
I'd try cleaning again with fuse wire ,then compressed air ,adjust the pilot screw if that doesn't work you could check the pilot jet size in the new carby and open the old carby pilot jet up to the new jet size if it's different ,someone may have fitted a carby from another motor.
I've used oxy tip cleaners to open up jet sizes and to check the jet size.
