I think seeing how fast you can get executed would be a fun category in the game. What do you guys think?

Maybe. The big issue with it is that you'd need to go through the rather lengthy intro every time

It's a good idea, but I agree with Denhonator, playing the game normally it takes 3 hours to go through the intro, that could go down to 2 hours if you skip the dialogue.

More like 30 minutes but that's still lengthy just to go get executed which probably takes like a minute