Assuming the ignition timing is correct and you get a nice fat spark on that side with a fresh plug, there are any number of carb related problems that can make it run too rich. Worn needle/jets, leaky float, float height, float hung up on gasket, etc.
Seeing as it is original carb, and you don't do many miles, it may benefit from a strip down and ultrasonic clean at this point. I would buy an Amal carb rebuild kit and jet removal tool and replace the parts on that carb that come with the kit. Also buy a new main jet and one smaller than you currently have.
Rebuild to current spec will eliminate worn parts. If problem recurring, then you can start changing heights, etc.
A detailed guide on dismantling, cleaning, inspecting, and reassembling the Amal Mark 1 Concentric carburetter.
amalcarb.co.uk