May sound a bit stupid. But I've used this product a time or two and had good luck with it. PBlaster it's called, a sprayable lubricant available at most auto-parts stores.
I've used it to free up a stuck spark plug. (could turn about 1/4" of threads) sprayed some of the stuff on, left it overnight and came out the next morning. The plug backed right out.
I've used it to free up a stuck bolt on a turbocharger housing. Sprayed the SOB good, let it sit overnight again and came out, still took some work, but I got it free without breaking the bolt head off.
So it may work in your case if you can spray it on without making a huge mess. Maybe after letting it soak overnight, an EZ-OUT extractor could be used to break the torx free?
Jeff