After some tweaks to the touch sensor measurement interval and threshold some more probe data was collected.  For 88% of the probes the range was 0.00 or 0.01 and 99% were 0.02 or less.  Much improved.  The mechanical changes are confounded by the software change from ESP32 to ESP32-S3 processor.  

As the copper pad engages to the bed the mylar does a good job holding it flat until the flex in the mylar causes it to touch the bed too.  With the copper pad mounted to the bottom of mylar, each arm contacts the bed away from the center point, resulting in the mylar wanting to raise the pad in the center.  Might need to change arm mounting holes to get mylar / nozzle height to sweet spot.