In order:
1. Dry ice probably won't help much. People also use heat. This doesn't seem to help the pins at all and doesn't do that much for the sight base. The best method is to get the barrel in a firm no bounce-no move set up and use a starter pin punch or a nail set to get the pins moving. Then use a standard punch to finish removal.
If the barrel is bouncing around or moving the force is dissipated and the pins may deform and jam.
The rubber hammer is the best method of actually moving the sight base, just don't beat on it until it deforms.
2. Reposting the barrel can work BUT, often it's just the front sight that's off, not the barrel or the gas block or rear sight block. In that case, you'd fix the front sight and screw up the rest of the barrel assembly.
Plus, the barrel pin is pressed in REAL TIGHT. They almost never drive out. They almost always require a large shop press to get them out. Usually, trying to hammer one out just screws up the pin and receiver.
Twist the barrel without removing the pin? Yeah, right........ First, it ain't gonna move, and all you'd do is really screw the rifle up. Second, HOW are you going to grip the barrel and receiver tight enough without really tearing them up?
If the barrel looks bent, check it by using a straight edge, and by looking down the bore at a vertical line on the wall. If the barrel is bent, the shadow down the bore will be "broken" and not continuous.
If it looks bent, send it back to whoever you bought it from.
Seriously, the correct fix here is to drive out the pins, bump the sight base over and re-cut the slots in the barrel. This is actually pretty easy.