In a remote session with an Adobe Tech Support engineer we discovered the issue was caused by the version of install media I was using. This was downloaded from the Adobe Volume License site in August of 2015 and the install files were dated 3.18.15. Updated to the 12.18.15 version of the installers and now Reader DC does uninstall as the last part of the install procedure, when using setup.exe to perform the install and with the customization wizard settings selected for Reader to be uninstalled.
Thanks for commenting, Bianca.
Paul