360 magnum troubles

Can you give us the piston model and the cam specs? It is not clear on how you set the cam timing. What is the cranking compression?

While the carb setup is suspect, it could also be ignition related.
Spark plug gap?
Ignition system type?

Does it die if you open the throttle very gradually? The pump shot sounds quite adequate for just coming off of idle; does the shot start the instant you move the throttle?