Convert varying voltage to resistance
The simplest way to do this may be digitally.  If you get a low cost microcontroller (e.g. arduino, but there are many, many options), you can use the on-board ADC to sample the control voltages.  Then, use either SPI or I2C to control commonly available digital potentiometers, which come in a wide variety of resistance values.

Searching for analog solutions to this problem, there are many posts on the subject - but none of them offers a clean, straightforward, universal solution.  While analog solutions are certainly possible, my guess is in the long run the digital solution will be both easier and cheaper to implement.  Digital potentiometers truly behave like physical pots, whereas any analog replacement will wind up with limitations (such as you noted above) that will mean you'll need to carefully consider how they interact with every circuit they are used in.