Sometimes, the only way is to bite the bullet, decide you are going to destroy something, buy the replacement, and go for it. ( a handful of replacement screws ? )
The worst anti-tamper screws are those one way flat blade style.
There's only three ways I know to get those out.
1. drill off the head, and extract the threaded stud that results.
2. You really don't want to know. ( involves a welder )
3. Make an impact tool, but it doesn't work if they are too tight, or glued in, and usually destroys the screw anyway.