If I could place the RX100 sensor in A500 for bird shooting, .........

It has nothing to do with sensor area.  A lens speed  is not, never has been and never will be based on the size of the sensor or film.  It is rated on the size of the physical characteristics of the lens - that ratio of is maximum entry pupil size to its focal length.

I was saying F15 is nearly four stops slower than F5.6 is where "4" came from.  I should have said nearly 3 but its not relevant anyway because the implication of your post is that the F5.6 lens loses 3 stops of light because you put in on a smaller sensor camera is nuts.

But that does not alter the characteristics of a 300mm F5.6 lens on any sized sensor.

No it won't.  In order for the longer lens to gather the same amount of light as the shorter one it needs a larger entry pupil size.

For ISO 100 a light level of EV15 requires an exposure of 1/1000 set at F5.6.  You do not have to modify that to be approx 1/125 sec because you put your F5.6 lens on a smaller sensor camera.

At ISO 100 a full frame user would have to set their 810mm F5.6 lens to F5.6 (and shutter to 1/1000) to get a correct exposure at EV15.

At ISO 100 a 1 inch sensor user would have to set their 300mm F5.6 lens to F5.6 and a shutter of 1/1000 to get a correctly exposed shot at EV15.

The implication of what you are saying as I read it is that you are suggesting that for a light level of EV15 an exposure of F15 and around 1/1000 sec will yield a correct exposure for the full frame user with their 810mm lens.

If so that is clearly wrong as that would give an under exposed shot.  You would have set the exit pupil to 54mm and that isn't large enough on a 810mm lens to give a correct exposure at a light level of EV15 if you set the shutter to 1/1000.