I'm unsure exactly what the "-safemode" switch is doing as I've not been able to find this anywhere in the documentation. However, I was able to determine that this issue was occurring due to some change between the way a package created on Windows 7 x64 behaves on Windows 10 x64. If I package the exact same apps, in the exact same sequence, using the exact same method on Windows 10 x64, they run perfectly fine on Windows 10 x64. In the past, I've typically tried to package for the lowest common denominator and only create OS-specific packages as required where compatibility issues popped-up. However, I wasn't expecting that to be the case with these simple apps.
In any case, I hope this helps anyone else who experiences the same sort of issue.
-Safemode causes the package to run in Disk mode, Legacy Registry, and disables Early Injection. You can find some information on Legacy Registry and Early Injection here under Troubleshooting properties.
I wish the Cameyo team would rehaul their documentations. So many support questions could be resolved on their own if more effort and love was put into the documentation. Every other solution I've tried has enough information, you could write a book on how to use their program, but cameyo, only has a handful of pages that are often vague in what they do, especially to inexperienced users.