I offer the following: should you lose engine power and wish to declare an emergency, then use the standard phraseology and terminology, which suggests that you state
Engine Failure as the cause of your predicament. Certainly on the airplanes that I fly, even an EPR shortfall is concerned an engine failure.
Furthermore, should you be absolutely hell-bent on the use of either "power" or "thrust," either word, preceeded by the word "engine" would suffice...? So yes; when any of the above terms are used intelligently, they are completely unambiguous!
I too have flown with people who's first language is not English. This particular statement, to me, implies multi-lingualism. That in itself, implies a level of intelligence somewhat above average. I personally (as a tri-lingual person) would hesitate to assume that English terminology is as ambiguous or confusing as you make it seem. Simple education in the correct use of the present terms is all that is required, as opposed to redefining the meanings of power or thrust.
Mutual respect on the other hand is something quite different. In my opinion it comes not from T-Shirts purchased nor thousands of jet hours, (which I too have done and forgotten about) but rather it is earned throughout a lifetime of reliable consistency.
With regards to my unconciliatory tone: I do sincerely apologise!