I think you have this backwards. Regular bulbs draw more power (current) than the LED's. Adding a resistor in parallel to the LED will simulate the load of a regular bulb and your stuff will work. The LED appears to be 'open' like a blown bulb, that is what is confusing the computer. Note, adding a resistor in series will cause a voltage drop across the LED and it will not work.
Measuring the resistance of a bulb filament won't be accurate as the resistance changes significantly when the filament heats up (like a glow plug). It would be very difficult to measure the resistance of a flashing bulb unless you can track current and voltage concurrently. I would just turn each filament on at a time, measure voltage and current, and calculate the resistance required. You can also calculate the same by knowing the wattage of the bulb filaments.