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.
The Notes On Rebuilding the Amal Mark 1 Concentric Carburetter page for the AMAL Carburetters website.
amalcarb.co.uk