I just swapped my panel out with a used one I picked up on ebay and it has fixed my problems. The panel was a good deal at only $65 since it was missing the touchscreen bezel and some of the plastic housing was damaged. I took the electrical parts I needed from this panel and installed them into the frame of my panel. Problem solved. Since this is a used panel of equal age as the car; I don't expect this fix to last forever before it starts to have the same problems again. I'll be trading in my Edge soon anyways though to get something more efficient for a new commute I'll be starting in a few weeks.
Regarding the idea of permanently disabling the faulty buttons, I'd be hesitant to try any irreversible modifications to your panel unless you have another replacement panel on hand as a backup. I also tried just unplugging the whole control panel from the head unit and confirmed the system will not work without the control panel harness connected. Putting a hole through a sensor might make the whole system go out of out of control since it will still be trying to control and sense the electric field for that particular sensor. If you're ok disabling all the touch buttons, you could maybe try leaving the ribbon cable from the touch panel disconnected from the PCB control board and then see how the head unit then responds to this.