mikewill,
The second engine in a piston twin was never meant or designed to be a get out of jail card. It was just designed to give you more options (prolong a glide, under ideal conditions, perhaps a positive rate after takeoff etc). Think of the aircraft as having one engine that is divided into two power plants.
Transport category aircraft (>5700 kg) are designed and mandated under legislation to perform on one engine. This is subject however to correct technique being utilized (especially a turboprop).
If you want to write a story, I suggest researching cadet schemes and low hour inexperienced Pilots occupying right seats of airliners. This is far more dangerous than a conservative Pilot flying a piston twin engine aircraft, who understands and plans for its limitations.
EDIT:
I see you have posted the legislation for light piston aeroplanes. The 1% climb gradient and maintaining altitude on one engine at 5000 feet etc is performed in a brand new aeroplane, with brand new engines, by a test Pilot with sound technique in ISA conditions (sea level, 15 degrees etc)
It is not performed in a 30 year old airframe (think Holden Kingswood) with a low time Pilot in Australian summer conditions.
If you consider a PA31 with a blue line of 106KIAS, at 1% that is 106 feet per minute. It will travel roughly 10NM by the time it reaches 1000 feet. The protection of an aerodrome for a CAT B aeroplane is only 2.66nm from the runway threshhold. It will generally not be able to climb to the 25MSA or the LSALT with that type of climb performance in the safe zone with factory new performance, let alone a 30 year old aeroplane!