Okay assuming legal immunity IS for real … could you really get to them in 24 hours?
Try out for the Philadelphia Eagles.
Me too, but I’d stick it in my own ass and use it to propel me around town.
First 4 hours or so I’m engaging a tattoo artist or airbrush person to paint my torso orange and crackly. After that I’m going all Ben Grimm and looking for the Yancy Street Gang.
That’s when The Wire suddenly and unexpectedly jumps the shark. 
So do I, but I’d be willing to, erm, ‘work outside the system’ in this instance.
But I figure that if I’m invulnerable and invincible, I can kidnap them both before the Secret Service can pull my mask off and find out who I am. I’d have to chain them in the basement until I could buy some rural property and construct my own private Spandau for them to live out the remainder of their days.
I’d be much kinder to them than they’ve been to the detainees whose treatment they authorized. I’d keep their cells heated/cooled to normal room temperature, would let them sleep normally for the most part, and would only douse them with cold water on special occasions.
Sure, I’m invincible, remember? (And I’m a loony, but that’s beside the point.) That’s in addition to being invulnerable. So my invincibility allows me to defeat the horde of Secret Service and whatnot defending them, and my invulnerability keeps them from harming me. So it should be no big deal to get to them.