If you are not going to accept the opening, or the close, of "Saving Private Ryan" here are a few other options:
Two from "A Bridge Too Far" 1) The paratroopers from the 82nd in boats crossing the Rhine near Nijmegen under murderous fire, making it across, storming the north end of the bridge before the Germans blew it up -- all for naught when the limeys slept while their boys in Arnhem were being massacred. 2) During the siege in Arnhem, the paratrooper who decided to expose himself to German sniper fire when the drop zones were overrun hoping to retrieve something of use (food, etc.) only to get shot and drop the container. It breaks and reveals the contents -- berets.
Or you could say Jefferson (Jim Brown) getting gunned down the "The Dirty Dozen" after dropping the final grenade into the bomb shelter air shaft. Surely if anyone could outrun Nazi fire, it was Jim Brown.