If the Joystick is fed with 12V, it puts out 6V centered, and swings from 4.8V to 7.2V. Here is a four opamp solution that produces the same amplitude, centered at 6V. It relies on a clean, accurate 12V supply.
It uses 12V rail-to-rail CMOS op-amps. First stage U3 just squares and amplifies the PWM signal so that it swings from 0 to 12V. The RC network produces a voltage whose average value is derived directly from the PWM ratios. It has a lot of ripple, so I pass it through a three-pole Butterworth filter with a cutoff of 1Hz (U2 & U1). The final stage U4 offsets the signal to 6V, and provides gain so that the signal matches the same swing as the Joystick. Varying R1 (65.5K, make it a fixed value in series with a trimpot) will center the swing at 6V.