The game checks for the next round triggers at the end of each measure, so it's not possible to start from a certain round. You have to let at least a measure of each "round" play first before transitioning. If you do it too fast, sometimes the song will desync.
I gave instructions for how to play back in QuattroPlay in IRC (though keep in mind that we won't accept logged VGMs from it)
Code:
start the song manually to prevent the playlist from automatically switching (press space to enter this mode, stop and restart playback with `s` and `r`)
then you can press 1,2,3 to switch between rounds. it will only work if you do it in the same order as the game, intro -> 1,2,3,2,3 etc
it's not possible to start the song directly at the second round etc, because those transitions are done by conditional jumps in the song (at the end of each measure)