I know it isn't exactly gritty or realistic, but I like to introduce moral quandaries through time travel.
At one point, my PC's had been sent back in time 500 years to deliver a sealed letter to Aurora, from Aurora, with an artifact that they knew wouldn't have the juice to get them all the way back. They were told that it could be recharged in places of great suffering and mortal death.
Long story short, they wound up stranded in new york in 1911, two weeks before the triangle shirtwaist factory fire. They were first torn between using the deaths to get back to the present and the temptation to save hundreds of lives, though they wisely decided not to alter events if it could be avoided.
In the process they:
Ran afoul of wardens and fled to never never.
Barely escaped that and wound up in chicago in the home of a serial killer.
took the train back to new york with only days to spare.
Broke one of the doors while scoping the factory out, and had to pose as door repair men later to ensure the exits could be chained.
Discovered a plot by subterranean creatures to enact an outsider based ritual at the factory.
Wound up starting the fire accidentally while trying to stop the ritual and collapsed the building.
Got back home to a mostly unaltered time line.
(This plot took inspiration from the Fandible dresden files podcast.)
Given that the setting is new orleans, how about time travel to pre katrina, when PC's could save a lot of lives at the risk of severely altering the time line.
