This application will actually allow you to stream any arbitrary internet radio station. It works with individual devices as well as Chromecast groups.
In this tutorial, I show you how to use your record player as the audio source (you'll need a Raspberry Pi and some other cheap hardware).
This idea, and much of my code, was adapted from the Vinyl Cast project by Allen Schober.
Open the application, enter the full URL of the audio stream you intend to listen to, tap the cast button on the toolbar, and select your destination.