This is what I used for years and years (it wasn't mine I borrowed it from a friend):
Ultimate Detailing Machine™ Dual Action Orbital Polisher
https://www.autogeek.net/udm-ultimat...g-machine.html
The BRZ panels are kinda thin so I haven't used a buffer on it, only applying compound by hand.
BTW battery will never beat a proper corded power tool.