Recommendation for project needing ~15 potentiometers

Presumably there will be an application on the PC which receives and handles the values from all these pots. In that case, wouldn't the simplest option be to buy the appropriate number of USB joysticks, chop the hardware around as necessary to give the user interface you want, and then connect them all to the PC (via USB hub if necessary)? Then the application can just treat them like joysticks using DirectInput (or whatever API is appropriate for the local OS), since that's what they are.