There is a lot of stuff in here......some of it I think needs my opinion also.
The "Rule of 500" is about how long one can image without noticing trailing in an unTRACKED mount. That is, one pointing to a specific point in ALT-AZ, and not following the movement of the stars by rotating on the right ascension axis. It is not about field rotation or polar alignment, or some of the other things mentioned.
It has nothing to do with the size of the sensor and it does not change according to pixel size. Now, that statement needs qualification. The image one gets on the middle of any sensor is the same as that of any other sensor as far as the amount of trailing, as far as the eccentricity of the star in the image. What may change is how many pixels that trailing covers. But the number of arc-seconds stays the same. When DISPLAYED at the SAME magnification, the center of the image will look essentially the same regardless of the size of the sensor. However, the outer edges of the sky will target area will show in the larger sensor and not in the smaller sensor. They have been cropped in the "crop" sensor. Now, if you pixel peep, and blow the pixels up, you will see that the sensor with the smaller pixels will show more trailing when counting the number of pixels in the star image......but the star will also show more pixels in its cross section. The eccentricity will be essentially the same.
If you add an eyepiece to the imaging train, you will increase the magnification of the image. This would have the apparent effect of lengthening the focal length. So that is fairly correct. This is properly called eyepiece projection, and is usually what is used in cell phone photography. Since the image has been magnified, the "rule of 500" no longer applies. You are right, you have to correct it.
Now, if you have a motorized mount, the equation has to change again. With an Alt-Az motorized mouont (not on a wedge), you can actually image longer than if you have a static mount. SO, you can safely use a "Rule of 1000," or maybe more (I really don't know how much more). And then, if your mount can be made to follow the celestial sphere, by rotating the RA axis or sitting on a wedge, then you can bump it to the "Rule of gazillions or something." (not really).
Where does field rotation come in? Well, if you would like to figure that out, may I suggest you go mess around with
You will see that Field Rotation is not the killer you might have thought. You can actually go for some time, even when somewhat misaligned. It depends on a number of things, including focal length, how far your guide star is from the center of the frame, and where your target is in the heavens.
Of course, all this "rule of XXX" depends on your tolerance for trailing. If you plan to display your pics on a cell phone, you can easily bump that rule to 1500, or 2000 probably. The stars on a cell phone are so small they just don't show much trailing. If you want to display that photo at 11 x 17, you had best keep it to the "Rule of 100" or something. (I made up those numbers. My point is, what you find the number to put into the formula "Rule of XXX" depends heavily on what you find tolerable. )
As one wise sage put it:
"Forget all the rules that follow".
Most fail almost immediately."