Sounds like the problem is not with the ignition but the power supply to the ignition. By jumpering the '+' side of the coil to the battery you are bypassing the ignition switch, ballast resistor, and wiring harness. Your problem lies somewhere there, you just have to find it. As to the coil operating at less than battery voltage, the ECU operates at full battery voltage but the coil is fed through the ballast resistor. I would recommend looking at the schematic for the ignition just to see where everything goes.

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