If they've got rust, then the rust IS damaging the drill bit.
Best is to A, dig the rust out with a pick as well as you can, B, drill slow and dry. If you've got lefties, smoke 'em if you've got 'em. Otherwise, whatever you've got, it's too small to get great results out of a lefty anyhow. The drill will break before it gets enough torque to unscrew "stuck" threads. Although a lot of times it's the washer face under the head that's really stuck, and a "sheet metal type" screw doesn't get "that" stuck anyhow...
Not sure where you're working on that convertible top, but if it's not ill advisable (and it may be just that...), but if you can, stick a straight punch inside the damaged torx head, and thwack it with a hamer a couple of times. (respectfully, choose the hammer and the effort level according to what's under that screw....). That shock, driving it in like a nail- Well, it won't drive in, but that shock can loosen stuck threads AND stuck washer faces under the head...
After those thoughts- Welcome to auto repair. This stuff was designed to be worked on until the warranty is up. After that, of course you still can, but the onus is on you, as the vehicle was never built to last forever... Start gently, and escalate slowly, and think several steps down the road at EVERY opportunity. You "want" this way to work, but where does it leave you if it doesn't.... 99 percent of these battles are about self restraint and persistence. The rest of the battle, with small screws, is a ten pack of decent drill bits when you'd usually just keep a couple at most on hand. They need not be that fancy. Just suitable for the minimal drilling you'd be doing in the material. It's the rust that kills 'em moreso than the metal. There's no screws on that car that you can't drill with the cheapest of drill bits, PROVIDED they've got a good tip on them.
There's another tip I suppose- Before going into a screw extraction, briefly test your brand new drills on "something". Make sure the point is good, center is good, both sides cut.... That'll wreck your day, and keeping centered on a screw stump is enough fun, you don't need the cross wind from "misbehaving" drill points