Well if the fancy computers say it's 1 nm between them it probably is
In the meantime, I had my head way too deep into this one, I think my explanation should be more or less correct now. My initial mistake was to make the calculation based on a E/W departure of 300nm; however, since the east/west movement is done throughout the flight, that distance will be greater. If it was done all at 30N it would be 519nm, as you wrote, and in my above calculation, I've assumed it to occur at the midpoint, ie 45N, giving a departure of 424nm. This also makes it easy to measure the hypotenus as you can design your chart to be scale accurate at that latitude.
From curiosity, the cos(45) is not the arithmetic average of cos(30) and cos(60). If we use the arithmetic average rather than the geographic average, we get a departure of 409,8nm and a consequent RLD of 1846,06 nm. This may be the way your computer calculated it.
But beyond this... I'm getting a headache. Long live the FMS
Edit: I see from that calculator you posted, that the results also do vary with which earth model you use (spherical or WGS84). Also, it probably does not account for altitude, I would guess. So I think we are down to splitting hair now.