I've now reread this thread, and I'm with PanteraDoug, try the simple stuff first. But if I read the post right, you haven't checked the timing? Putting the dist back "in the same position" isn't accurate enough. And yes, an engine with too late timing will backfire, especially when getting a little throttle, and will run miserably.
So, set the timing, before you start to tear stuff apart and buy lots of stuff.
Other good advice from above: yes, read the plugs. Wet with fuel means either too rich a carb or no spark. Bone dry means no fuel.
Last general advice: To check the carb, put on another, you probably have one on the shelf or a friend has? Same goes for dist/ign box. But one thing at a time, this is trial and error until it's solved.
But first things first, how's your timing!
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