Thus enters my favourite file manager, Solid Explorer. They now have a plug in for their app that allows you to share the file to the Chromecast!
You need to have the trial app (FREE), then the paid unlocker ($2)... then the add-on for the Chromecast (FREE).
Just browse your files and tap one to choose to "Solid Explorer Cast" to open it.
Right now, you can cast only media files (pictures, audio, video)... but here's hoping that you can eventually do this with other files... say a power point or something!!
Total upside is that you have a kick ass file explorer as well as a 'caster'.