Kevin,
The original spec for Monobloc carb on a Dragonfly was: Main Jet 130, needle 3rd notch, pilot jet 30, needle jet .1065, throttle valve 3½ cutaway. Those were the settings for the fuel available in the mid 50's - our modern unleaded rubbish usually gives better results with an increase of 10 on the main jet, and a 3 cutaway on the slide. You could also try a slightly richer slow running mixture.
The fact that your engine starts but then dies, suggests there may be an air leak on the inlet manifold - possibly on the inlet tubes if they have been re-chromed (the polishing will have reduced the diameter of the tubes). Try applying a bead of silicon rubber around the tubes where they enter the end fittings (leave it to cure for 12 hours before starting the engine) - if that identifies where the leak is occurring, you could try fitting some 'O' rings with a slightly slightly fatter section.
Regards,
Eddie.