The best wya I think to get Spotify connected to Chromecast is to use the Spotify to MP3 Converter. Thus, you will be able to syns the Spotify music files to your devices for offline listening and also move to other software. You can then keep the songs from Spotify forever. I like it.
Did you guys try Spotcast?
Was recommended to me here
and from what I read it should work. However I was not able to try it yet becaus of …no time 
Thanks for sharing! I would like to have a try.Did you heard about the Spotify Music Converter called Tunelf ? my friend had recommended this software to me.
In order to use Spotify with Chromecast, I use the DRmare Windows Music Converter for Spotify. It supports to use Spotify music on any other devices directly with original quality offline. You could give it a try if you are interested in it.