Ok, I wanted to update everyone on what I found and how I fixed this. Hopefully it will help someone else with the same issue.
I decided to go back to my days of laptop repair, when certain brands had hard to find drivers. I located the vendor and product IDs (2341 and 003E respectively) of the Arduino Due in device manager, and googled them. That took me to this thread on th Arduino forum: https://forum.arduino.cc/index.php?topic=131100.0 where someone was having a similar issue with actual Arduino boards. The fix is to make ANY arduino driver version match the hardware you have by changing the vendor ID/product ID to be a less accurate match, causing the driver to match the hardware more loosely. I used the 1.6.1 version that I had recently downloaded, edited the arduino.inf file, and changed the following lines:
[DeviceList]
%DESCRIPTION%=DriverInstall, USB\VID_2341&PID_003E&MI_00
[DeviceList.NTamd64]
%DESCRIPTION%=DriverInstall, USB\VID_2341&PID_003E&MI_00
to this:
[DeviceList]
%DESCRIPTION%=DriverInstall, USB\VID_2341&PID_003E
[DeviceList.NTamd64]
%DESCRIPTION%=DriverInstall, USB\VID_2341&PID_003E
I saved the inf file as a different name, then deleted the device in device manager and hit rescan. This time it found a driver match and installed it, assigning the printer USB to COM3. YAY! I was in. From that point, setting up Repetier-Server the rest of the way was a piece of cake.
Happy to be printing again!