How to fix APi/aPK error when trying to run 4.16?

Yes, installing with the NVPACK/Chooser as opposed to the NVPACK/android-sdk-windows/android-sdk-windows/SDK Manager seems to do the trick.
The former installs the APIs to NVPACK/android-sdk-windows/platforms, while the latter installs to NVPACK/android-sdk-windows/android-sdk-windows/platforms, where Unreal does not find it.