Thanks, Steve. That Shoutcast seems interesting -- guessing it's super stable if that's what you use for the archive. I tried injecting the url into the VLC app, but no dice.
I did find a pretty awesome (and free) solution, though. There's an app called VRadio, which let's you listen and record. No live DVR-style rewind (which Audacy and I think the paid version of TuneIn has), but for now that's okay. You can even schedule your recordings (12-3, M-F)
First station I tried was CBS Sports 1270 in Detroit. But when I listened to the recording, it was, unfortunately, another annoying Audacy/BetQL station with Nick Kostos ads. The next day I tried WTKA 1050 in Ann Arbor, and it was exactly what I was looking for. Regular old CBS sports radio -- it even has Andrew Bogusch sports updates during commercial breaks. No BetQL garbage. So yeah, VRadio and WTKA 1050 -- good stuff. I'm using the Musicolet app to play the files, btw. Unlike VLC, Musicolet never forgets where I left off. And yes, I know I'm a weirdo haha.