Casting from NTS (or other) apps

I'm loving NTS, became a subscriber last year and it's replaced 6 Music as my main station.

One major problem I have is that my whole setup around the house uses Chromecast Audio devices. I can cast most of the live content using TuneIn, but I can't listen to previous broadcasts this way, or some channels not on TuneIn. This wasn't a big deal at first, but now I'm starting to get to know my favourite DJs, I want to explore previous shows.

Is there any way I can cast everything from NTS using my phone? Bluetooth isn't an option.