@Thedirge - Look for an old drill press with variable height machine head - or an old vertical milling machine with variable height machine head.
You'd need to set limits on vertical height adjustment of the fore end rest.
Also develop a pinion arrangement that could be operated, without interfering with the joystick handle.
As you say - it could be done.
As @6x47 says - it could be done but how much $$$'s are you prepared to spend?
More than the cost of a standard rest?
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