How about hotwiring?, a direct feed from the battery to the coil with a switch in the wire. With the switch in the off position go for a ride around and when you get the problem of non starting then switch on your hot wire and try starting with the starter.
If it starts off the hot wire then you will know that the ignition switch is not providing enough power to the coil when the starter is engaged and a ballast resistor may help.
It would appear that because it starts with a bump start it is coil related or starter drain on the ignition side.
Phil
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