Hi Adam,
Thanks for the very clear photographs of the electronics. The problem is a grounding issue, as the pickup shields are not connected to AC ground. The long wire insulated with the teflon sleeve on the wiring side of the circuit card is the common / ground lead. Somewhere along the way, the pickup connectors have been rotated, so the pickup lead center (hot) terminal is connected to ground and the shield contact is connected to the input (hot) terminal to the pre-amp. Note that the pickup connector has been inserted while orientated with the two slots visible on top, and we need to disconnect the pickup connector, rotate it 180 degrees, and reinsert it with those slots down, so the smooth side of the connector is on top. Do that for both pickup connectors.
-ron