Did you check that the cut out wires in the carby aren't shorting out.As when the rubber boot wears the wires can touch causing the very same problem as you have.As for back firing it could still be the decompressor valves as usually it is compressed air escaping through them.
They were know for coil problems but you usually loose spark for the back and the front usually has some sort of spark.I'm not sold that it is a coil issue.
Did you check the points?
vccomm not all twins had points some did have electronic ignition.
