I only have the analog pins left, but my problem happens with both analog pins AND PWM pins (tried both ways).
The analog pins are just analog if they are inputs and PWM is only an output functionality. Please define how you want to use them as a replacement.
When I use pulseIn to read the values, I get oscillations (for example when my joystick is in the 0 position, values oscillate around 1045, but with a difference +- 50... which is pretty big).
How do you read a joystick with pulseIn()? Please post a wiring diagram.