"The engine is out of tolerances as per flight and maintenance manuals."
No multi engine experience here...but I cant even imagine a Tech. manager that refuses to change and engine that is not up to spec. (assuming that the torque/ temp/compressor speed indication systems have been checked?)
Seems that it would be much safer to figure out the problem in the shop....in this day and age of litigation I would have to wonder if in a court of law a pilot would be held responsible for flying with an engine that is know to be less than spec.
Seems to me that you need two things....a new engine (at least till the problem is isolated), and a new Tech. manager!