Before you paint, try this:
Polly S Easy-Lift-Off (ELO)
This stuff is pretty amazing. I collect old slot cars from the 1960's.
Sometimes I find a rare and potentially valuable car that has been
painted by a previous owner. I put this stuff on the undesired paint.
The paint gets soft and loose and can then be worked off. It's not
effortless but it's really not that hard to use. It might be easier for a
guitar case because I'm usually dealing with delicate plastic cars that
I don't want to damage in any way. I've been able to restore some
difficult-to-replace old cars.