Here's what I would do:
1) Go to a public restroom, where there are metal dividers between the stalls. You want to be between two metal dividers, not next to a wall.
2) Sit down, prepare for battle. Maybe take off your belt and bite down on it, if you've got expensive dental work.
3) When the shit goes down (har!) start pushing on the walls, hard. As you cramp out your demon shit, you will naturally to push harder, and very likely begin to yell, involuntarily. By the time you get that fucker out, you may have broken one of the walls. You would be surprised at the scary wild animal strength you can muster when you're trying to shit out a watermelon.
4) Post-workout shake.
If you do manage to break a wall, you can at least take solace in that for the next couple days while you're checking the TP for blood.