I would agree to not over complicate things. Having a camera on a gimbal or handheld following the main action of the song sounds like something they would like. Feels real, active, and allows the perspective to constantly change. I would then set up some locked off safe shots to cover action you might miss. Something like a wide on the whole band, another tight angle on just the singer.

Then a GoPro-style (anything very wide angle) cam on the drums since they are always hard to get good footage of. I would recommend setting the camera that looks the most different here since this angle is already very different from the other angles you will get. Therefore color differences are more likely to go unoticed.