There's a problem in the wiring from your ignition switch to the coil. How do I know that? When you jumper the battery to the S terminal, the starter solenoid also puts out full battery voltage to the coil, bypassing much of the ignition to coil wiring, not not all. The infamous pink resistor wire, located in the underdash harness, lowers the voltage from the ignition switch to the coil from full battery voltage to 9V or so. If the voltage is much below that for whatever reason, the engine will not run well. Since it runs good with full battery voltage, that seems to isolate the problem primarily in the underdash harness or the connector to the headlight harness, or from that connector to the engine gauge feed plug near the firewall. That's where the junction is from the I terminal on the starter solenoid to the main coil line is joined (bypassed).