You're correct, it can't be done because of this formula (well not because of the formula, but the formula results from the physical reality that prevents it):
Power = ( rpm x torque ) / constant
The constant will change depending on what units you select for power and torque.
So yes, that's the tradeoff you mentioned... The only thing that might come close depending on your application is possibly a continually variable transmission (CVT)? That would allow you to run your motor at a fixed RPM while changing the output speed. As it has an effectively infinite number of gear ratios you can tune your setup for either, say, peak efficiency for peak power output, etc.
Absolutely not going to fit all applications, however.