You know a few things that may be helpful to identify the problem: bypassing the wiring to the ignition switch allows it to run; however, with the bypass in place the ignition switch does not disconnect the ignition to stop the engine; the e-brake switch kills power to the ignition; and the problem happened while driving.
The e-brake switch killing the ignition seems strange but unless the switch was somehow actuated while driving it seems unlikely to be the source of the problem.
The bypass to the ignition switch that allows the engine to run is promising but the fact that the switch does not shut off the engine indicates either the jumper bypassed the ignition switch (connected directly to the ignition) or there is a problem internal to the switch. Next step would be to confirm what the bypass is actually connected to on the ignition switch. If it is connected to the battery terminal look into a replacement ignition switch, if it connected to the ignition terminal, change it to the battery terminal to determine what changes.
