Move servo relative to current position (analog)
I still would try to use a microcontroller, that's going to be the easiest solution. Do you plan to remove the sensor inputs and the servo output from the controller? That will give you 4 extra pins. Isn't there a device in the same microcontroller family with a few more pins?

Alternatively you could use a small separate microcontroller to handle the sensor data and servo. That will be more compact, cheaper and easier to control than solutions involving 555s and what mores.