If an engine that has failed could be used as a ram/rocket jet engine, the argument would be no more. These sort of engines burn alot more fuel in shorter periods, which means that you can get rid of all that fuel you'd like to get rid of, and at the same time generate enormous thrust that will enable the aircraft to climb. If engines could be designed in this way, the one engine inoperative problem would be no more.
I'm putting a copyright on this idea
Ram engines do not and cannot work on low airspeeds/takeoff.
Rockets do, but they require oxidizer tanks and systems.
My suggestion is use the good engine. Reheat/afterburner on a bypass engine is a known procedure. It is extremely inefficient at low speeds (at high speeds reheat is actually better than turbine!), but it has the advantage of being inherently simple, lightweight and reliable - you could have an engine which is lightweight and efficient in cruise but has immense thrust/weight with reheats on!