Could QMIDI be able to move between Markers on a cue system?
One thing that might need to be added is an extra degree of resolution for the timestamp field... 1/100th sec resolution is fine for lyrics, but a cut and jump point might need 1ms resolution to not interfere with the groove. (EDIT... Most DAW's have a 1ms or better position accuracy, so an easy cut and paste into the edit field should give glitch-free transitions)
But given that, it shouldn't be hard to place Markers in the List Edit and have a simple 'Move to Marker(x) at next Marker point' which would do away with the need for a tempo track if you wanted to do it at ANY bar...
Then you could break the backing down to things like Intro, Verse1, Chorus1, Bridge, etc. and have those mapped to function keys (which could also be mapped to a bluetooth pedal) allowing live restructuring of the song.
Mind you, it strikes me that a Marker put in at EVERY bar start, along with a filter for display that you could restrict to just the Markers at structure points would allow one to jump to a Marker from any bar in the song! Hmmmm... There's a lot of possibilities to this function, if added!