If the checklist says to shut down, that's what to do. Overweight landings are when you're on fire and want to get off the jet asap.
I believe that most twin aircraft c/l's say "land asap" after an engine is shut down., That's what to do.
The bottom line is.. when the proverbial Poop hits the Turbofan, I am more inclined to consider the Check-List before the Cheque-Book !!!
Better to do the right thing and lose a bad job than do the wrong thing and throw away a great career !!!
Blue side up!!!