If interruption is ok, this approach is the most doable.
If you are using a live stream, or if your player can handle positioning and position update events, you can make the page-reloads fairly seamless as well by auto-playing at the same position you left the prev page from.
That’s an interesting scenario I’d have some fun looking into. If you want to PM me with some details, your site link, the player you want to use, and the audio stream you’re connecting to, I’ll look a bit deeper and see what it would take for me to build that for you.