There’s a sort of order from least to most destructive:

Exactly correct driver >
using an elastic band or other thin piece of rubber, between driver and screw, for grip >
different screwdriver that fits differently (e.g. a small flat driver in any cross-headed screw) >
again, with elastic/rubber >
other, unlikely drivers >
other grippy options, like steel wool >
superglue the driver to the screw >
epoxy resin a driver to the screw >
cut a new flat-head into the screw head with a dremel >
use a screw extracting bit >
drill out the screw head >
cut or drill out the plastic surround

I’m sure there’s other options I’ve not remembered. A lot of it depends on which screw is stuck, and how accessible it is.