@Rob, I got the LaunchScreen.storyboardc to work, but there are two things you should consider making more clear in the online document at https://docs.coronalabs.com/guide/distribution/buildSettings/index.html#launchimage
1) It might be worth mentioning that the sample project is an XCode project and the storyboard file is NOT included in the zip file list. You MUST launch XCode and do the EXPORT. Perhaps this should be obvious, but I'd still recommend making it more clear, especially for those of us who really never use XCode for anything - I used to use XCode to see console messages via 'devices', but now I've found using the Applications -> Utilities -> Console.app much easier, so really, I never have to use XCode - and isn't that one benefit of Corona (non-Enterprise)?
2) Also, another important worthwhile point is to know that when you export from XCode, you need to export the 'package', not just the storyboard. This will result in the proper filename "LaunchScreen.storyboardc" - whereas the 'c' at the end is missing if you don't export the 'package'.
3) It may also be worth mentioning that after putting "UILaunchStoryboardName = "LaunchScreen"," in build.settings in the iPhone - plist section, that we can either remove or block-comment out the uilaunchimages section using --[[ and --]]
If these two points were more clear in the docs, I wouldn't have had to bother you so much. So, please accept my apologies. Hopefully this feedback will be helpful.
I love Corona and the amazing technical support work your team is doing. Seriously. With the new version of Play The Bible Ultimate Verses due out by the end of April, many have told me it is the most sophisticated Corona-based game they've seen. If there are any features I've implemented that you feel may be of benefit to the community, just let me know and I'll do my best to keep contributing to this amazing, thriving community of developers.