I think the Hardware Playthrough is a legacy service no longer supported. Software Playthrough, with the delay, is the only service I’ve ever seen work.
This is also why we recommend listen to the device rather than the computer, if you can. If you’re set up for overdubbing or multiple track sound-on-sound, it’s required.
Since you’re probably going to cut down the music into individual tracks in post production anyway, why is this critical? Please don’t make a common mistake of capturing directly into MP3. Do everything in WAV (Microsoft) as an archive and/or Audacity Projects and then edit, and then make the MP3s or whatever else you want.
You can’t generally edit MP3s without the quality decreasing.