I have created every splash screen and icon in the list at https://msdn.microsoft.com/en-us/library/dn757053.aspx. They all reside in the correct folder.
It works nicely on Android, but on Windows Phone I still get the Apache Cordova logo when the app starts.
How do I approach debugging this?
When Cordova creates your VS project it creates default splash and icon files in the platforms\windows\images folder, so that's where you'll find the rogue image you're looking for. Just replace that with your own file and you should be good to go. In my own Windows 8.1/Windows Phone 8.1/Windows 8 VS solutions, the two splash files I replace are: