I usually edit the song track and put three loud bleeps for three seconds (so one bleep per second) before the song starts, and burn it to a CD and use it for playback, so that way, all you have to do in editing is synchronize the bleeps on your timeline with the bleeps in the audio from the footage.
You can do that with a TC BWF instead of TC DAT. Even though DAT is dead, a used TC DAT recorder still cost as much as a new 702t. You could rent the DAT but it still would seem to be more hassle then just renting or buying a 702t or even HD-P2.
Also cueing up a file is much quicker/simpler then a tape.
Several suggestions for playback recording.
1. Be sure singer SINGS! Singer should actually vocalize the words. Moving the mouth without speaking looks different and noticeable.
2. Use earpiece or place monitors as close as possible. Remember rule of thumb - 1ft = 1ms delay.
3. Create playback file as 48K and record playback music to the camera on one track.
4. Where possible use boom mic to capture singers voice for a post guide track to compensate for possible errors. Place monitors to hit the null of the mic as much as possible.