I suspect that you do not understand what John is quite accurately asking for. So I'll give you a few simple tests that you should do. I suspect also that you do not have a schematic of the potentiometers used in your joystick nor the schematic of what you wish your joystick to connect to. So this is how to test their source and input impedances. The simplest analog joystick signal will be just a potentiometer. It maybe easier to power your joystick with a separate supply for these tests. Now power your joystick without connecting it to your controller electronics. Measure the output voltages with a high input impedance device like a digital volt ohm meter at mid-point setting, fully forward and fully backwards. (This might be what you already did but one needs to know the test circuit , not just the numbers from the test.) Now return to your mid-point position. If you add a fixed resistor now in parallel with your volt meter and the voltage drops precisely in half, the resistor you added will be the output impedance of the joystick at mid-point. But don't go nuts trying to find this by putting in different resistors. As long as a significant voltage change is noticed, recorded and the fixed resistor value is recorded; the output impedance of the joystick can be calculated. With the load resistor still in place, record the new fully forward and fully backwards settings. (Sometimes the output impedance significantly changes with an analog signal.)

Now to measure the input impedance of your electronics will be similar but with less steps. Take a AA battery and record the voltage across the battery. Add a series resistor to the battery and connect this resistor and battery combination to the input of your electronics. Once again when the voltage at the input electronics is exactly at half of the battery voltage, the series resistor has the same value as the input impedance. If a 510K series resistor will not drop the voltage in half, we'll just accept that you have a high input impedance. This may happen.

Once you return this collection of data, I'm certain a simple accurate circuit to meet your needs can be fabricated.

(I do wish that people who start a question would have to sign in with a name.)