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On your account on your phone, make a playlist and download it (sth like "for offline use"), then go offline at work. Limits what you can listen to spontaneously, but you can simply take one of the "radios", copy to playlist, make offline at home so you download over wifi, then remove and repeat for each day. Nature finds a way.

I think there are some web services which open up a web page in a specific browser version and stream that back to you. Perhaps you can try and have them run it in a newer browser.

I can't name a site off the top of my head, but googling will probably work.

The obvious thing to me seems to be BYOD e.g. smartphone or tablet you can stash in a drawer or keep in your pocket while using it for Spotify. I guess you've already thought about that and it's ruled out for some reason.

Listen on your mobile device.

Haven't used it, but perhaps Tizonia?