I have some ideas and suggestions that might do it. For simplicity’s sake I would use a MIDI file because using an audio file requires binding to the track speed adjustment on the media player slot and is not as accurate. Record the MIDI file at the tempo it usually is performed at using a DAW or Cantabile set to that tempo on the metronome when recording it. The tempo value will become part of the MIDI file and will allow it to sync with the metronome tempo later when you want to alter the tempo.
On the media player you use to playback the MIDI track set the sync to Musical Slave.
Then create some bindings, one for the tap tempo for the metronome and one for the Transport Play.
So in use you would count in the song at the approximate tempo the backing track was created at and start playing the song. When you get close to where the backing track is coming up you tap a momentary switch type damper pedal a few measures to catch the tap tempo in C3. Then press the play button on the Main transport on the first beat song where you want the track to begin playing and it will play back at the last tap tempo you entered with the tap tempo pedal presses. Incidentally the tempo of the playback can be altered by re-tapping the tempo in real time. I set the tempo settings to Dynamic, it catches the measure tempo in real time from the presses no averaging. You can try the other 2 set tempo detection modes to see which one works best for you.
Hope this helps