Hi Phil,
I assume that your linear actuator has a positional feed back potentiometer giving a signal of 0 to 5volts back to a motor controller that receives an external position demand signal of 0 to 5volts.
Malcolm and Subculture's idea of using a low power ESC to give pulses with less gaps than in the original PWM, would give a faster response than just trying to integrate the 1 to 2ms pulses every 20ms. If it was a programmable ESC, you could calibrate the output to your exact need of 0 to 5 volts range for 1 to 2ms input.
I needed a 0 to 5 volts signal derived from RPM pulses for a motor control system and ended up programming a PIC micro-controller to do the job. It was very accurate and had a fast response. The PIC has its own high frequency PWM output much like an ESC, which I integrated with a simple resistor-capacitor network and fed the signal back into the PIC's analogue input. The PIC then ensured that the output was correct. I also have some PIC software that measures the pulse length of a PWM signal from a radio-receiver and stores the signal as a 0-100% value. This percentage value could then be used to control the analogue output voltage.
The PIC route is a totally over the top for your application and I would think that a cheap servo driving a potentiometer (say 10k linear) through a shaft will be the most practical solution.
If you had a supply that was higher than the 5 volts required, then a small trim potentiometer could be placed in series with the servo-driven pot and adjusted to give exactly the 5 volt range required.
Ian