Just an update. I sent an email to the tech support team at Millonetech, and we were able to confirm that the eTape sensor I am using is not a resistance to voltage module (as I suggested above), but contains a simple voltage divider. This version works fine with 5v VCC, so that is not a problem.
I purchased some 100k resistors and will build a 1/2 voltage divider tonight. I will let you know if I am successful at eliminating the strange behavior.
Thanks for your help.