Might be doable, but would be a workaround:

  *  Start a background `streamripper` process whenever playing a station.
  *  Let it spool mp3s in a dedicated directory.
  *  Recurringly delete anything older than 15min.
  *  When JIT recording is requested:
        #  simply extract the latest mp3 (or wait till it's finished)
        #  or even just open up that temporary mp3 directory for copying.

Managing a background proccess might be more work, but seems feasible. (Maybe research if existing audio players already offer a similar functionality instead. It's a workaround mainly because ST2 does neither manage playback nor recording.)