For anyone that cares, I finished quest mode a few days ago. The easiest way to do this was to play Legend of Max, Sakura, or Outer Limits on Heavy to obtain the lower fanbase flags. Then, as you buy background dancers, you gradually earn more points per song, so you can get those higher fanbase flags. You can see your items in the Options > User Profile > Quest Mode screen. (WTF were you doing Konami when you did that?!) Instead of actually dancing through all the songs, I used the controller to spin the control sticks rapidly, easily clearing each song AND getting lots of points to walk around with. Once I had all the flags, I went to the Rhode Island section of the map, because traveling between these cities only cost 120 points; basically the cheapest place to move. (Easiest, cheapest way to obtain all those stupid puzzle pieces)
Phew...what a speel. If anybody needs any help with it, I can now provide some! Good luck if you decide to dredge through it, though to get all the songs and dancers, you must.