Apparently it is quite possible that applying the Cumulative Update causes this issue, so I need to remove my Appx BEFORE applying the Cumulative Update.
New-OSBuildTask -TaskName "Win10 1607 x86 Appx"
So I delete my OSMedia 1607 (with the CU) and go back to the original imported version. I then create a New-OSBuildTask and select Windows 10 x86 1607 only remove Appx Packages, and nothing else. When testing I choose to always start with x86 as it is smaller, so I get results quicker.
I will now Invoke the Task with -ExecutionMode "Execute Stepped"
Execute Stepped
This method adds several "Press Enter to continue" stops throughout the process. This allows me to target the specific action that I am looking into. Additionally, since I am still mounted, I can perform some other testing.
Results
I guess I just confirmed that Appx Packages can't be removed Offline on Windows 10 1607. It seems that the original release was able to, but subsequent released can't.
But Remove Capability works fine!
So no removing Appx Packages from Windows 10 1607! I won't make any changes to OSBuilder to address this as you may have a version older 14393.447 that does work properly.