I sais it once before, you need to get the wiring diagrams and fully understand the speed control circuit.... If after that you still do not fully understand the circuit, how it operates, and how to diagnose it, you should give up and take the car to a profesional....
That said, I think the problem is at your resistor.... By bypassing the resistor at the connector, you got the car to run correctly right? That tells me that all the relay connections etc are all OK, the car was commanding the fuel pump on via the resistor box. So when you add the resistor box back into the mix, it stops running correctly...... why not replace the resistor box? Also make sure the connectors all look good, are not burned up, corroded, etc...
It is remotely possible that the fuel pump is getting bad, and does not want to run at lower speeds.... but the resistor box is a lot easier and cheaper to replace than a fuel pump, so I would try that first....