Solution! Time-shift an early broadcast of This American Life on the internet. That way, it's available for you to listen to when it's convenient for you. For me that's usually on my iPod, on my Saturday run.
The earliest reliable and listenable stream I've found is on WUIS in Springfield, IL. It airs on Friday evening at 7pm Central time. They provide a quite listenable 56k stream at this URL:
http://war.str3am.com:7780/wuis.mp3It's great for me because I am on the west coast, so it comes on at 5pm my time and is available at 6pm. There are earlier internet broadcasts of This American Life on east coast NPR stations, but I have found their streams to be too low-quality or unreliable.
If you know of an earlier broacast that's of decent quality, let me know in the comments. Whatever stream you use, be sure to donate to the station to compensate for the bandwidth. And of course, donate to This American Life!