Please don't get offended by challenges, Flecc, it goes with the role you've established for yourself.
Continuous power as a legal definition is even more subject to questionable interpretation than average power. Here's an example:
In the aircraft world, engines have a rating known as MCP, maximum continuous power. Several key performance factors can be linked to MCP, nowadays the most likely figure is specific fuel consumption. This rating can also have legal implications for things like certification.
One easy way for a manufacturer to make his product seem more attractive in these fuel-efficiency focussed times, or to allow it's fitment to an airframe that would otherwise not legally be able to take it, is to just arbitrarily adjust the MCP figure down a bit. This will have no practical effect on performance, but will reduce the SFC figure that he can quote in advertising, or, perhaps, allow the engine to be fitted to a type that might otherwise have not had enough spare empty weight to use the engine.
What's this got to do with ebikes I hear you all asking? Easy, all a manufacturer needs to do in law to comply with the "continuous power" rule is print a placard that states what it is. In practice this is what many ebike manufacturers do. Just look at the motors that are advertised as being rated at 200 or 250 watts. Do their controllers limit current to the low values I mentioned above? Of course they don't, most controllers allow motors to absorb at least 500W, many will supply far more power than this to a motor.
Even the tiny little Tongxin motor that I'm running has a placarded power limit on the motor - it reads "rated power 160W". The label on the equally tiny controller, however, reads "36V, 15A", meaning that the motor can actually take 540 watts. I know from personal experience that the motor will take 15A at 36V for long periods of time without getting warm. It's obviously got a practical continuous rating that's a lot greater than the stated 160 watts, but only the manufacturer can stipulate what the continuous rating really is.
If I were a motor manufacturer, then I might want to be very sure that my motor would not overheat if it was operated in temperatures of, say, 45 deg C (typical mid-summer temperatures in some middle east countries). I might well build in a safety factor to the rating to allow for this. The motor would then, accidentally, be capable of operating at a very much higher continuous power level in temperate climes, but would this render it illegal?
The EAPC law is so full of ambiguities and loopholes that I don't think there's the slightest chance of anyone being successfully prosecuted purely on the basis of the power limit. The same can't be said about the maximum assist speed though, as that is relatively simple to check. As I posted before, it's quite easy to show that if speed is limited then the "continuous" power is as well, in effect.
Jeremy