I'm curious, is there an undocumented flag or anything that causes the periodic output of Gatling to go to STDERR so that I can capture the output of a scenario and direct it to a file, and JUST get the println output generated by the scenario?
Nope, there’s no such hidden flag 
But you can set the System.out to something else in the Simulation.
If I did that, wouldn't the periodic updates still be written to the same stream as the println() output?
Actually, I don’t think I get what you’re trying to do.