Use montage: Put the music on track 1, copy this clip to track 2. Adjust size of clip on track 1 to ~20 seconds, and adjust the start of clip on track 2 to ~10 seconds (or the values that best suit your needs). Apply clip FX for tape effect on clip 1, and EQ on clip 2, and create a crossfade between the clips. You could also do this in one track.
If you keep both clips at the same original starting time, and only adjust borders for both, they will remain exactly sample accurate. Just don’t move an actual clip in the timeline. If you want to move clips to different tracks, just grab them while holding shift.
There are several ways to skin a cat. I just thought this question had an easy answer without even using the montage and the more involved procedures to accomplish such a simple task. But perhaps I didn’t understand the OP’s question.