Been reading some of the posts about some folks trying to cut out ABS or styrene armour and thought this might help. It's a Monodex sheet metal nibbler. It was made in England. I got it about 20 years ago, so I'm not sure if you can still get them but they are really awesome. It was designed for cutting out sheet steel for car repairs so styrene certainly doesn't worry it too much. There's probably an equivalent product on the market for you folks in the States, I guess.
For what it's worth. Phil