It is more important to remove the undercoating that is already lifting as moisture can creep under it.As I removed some of it there was surface rust underneath.The really hard to remove schtuff will have mint paint/metal underneath.As mentioned,leave the really good stuff on.I did.
P.S. I wear a face shield and my worst clothes.I also lie down on a foam mat to be somewhat comfortable.
Keep your beer away from the working area,too!! Nobody likes black chunks in their favorite brew!!