Thank you, and I really do mean THANK YOU for your most detailed reply. I agree with everything that you said. I am an electronics engineer myself and have spent years attempting to reduce noise and radiated emissions from designs. I believe that I needed the "push" from you to awaken me to the realities of what noise can do in a system.
In reference to noise reduction and ground return issues, I have the Altium schematic and layout tools and have downloaded the Altium schematic/layout files. I see some problems with ground returns. If I might, I would like to ask your advice on some specific issues that I am sure you have encountered since you know vastly more about the Arduino than I do.
First, it appears that there are two sources of +5 volts. One comes from the USB "USBVCC" and the internal voltage regulator. I propose that as long as the use of current from the USB driver on the PC can be limited to below, I think 500 mA, then the internal voltage regulator should not be used at all. Otherwise, there are two complete return loops for ground. That can't be good.
Second, from the data sheet of the Atmega2560 IC, the analog voltage reference for the A/D converter are provided, on chip "VREF". Usually I don't care for this type of configuration unless I can control the decoupling in the layout, myself. I propose, and yes, I am going to be very "anal" about this, that the ground of the USB be connected, via a thick, conductive wire, to a copper bar outside of the Arduino (and isolated from the chassis), giving the ground some mass. Then the other important analog grounds can be connected, again, with thick wires, to this copper bar. Decoupling caps can be added, on the Arduino board, as close to their "use point" as possible.
As you suggest, I need to replace the copper wires connected to the rotary potentiometers with shielded wire and decoupling at the connection point at the Arduino.
I do not have noise free HID controls. I'm using a console from a 25 year old Precision Flight Controls simulator. It has a good feel.
I do not understand how to add the quadratic function that you mentioned into the calibration routine. Can you elaborate?
Also, the SImVim analog function includes non-linear option (quadratic) that you can set (but it needs to be added to the calibration window as checkbox).
Do you agree with my proposed analysis?
Thank You again