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Chris,
Using similar triangles, I've done a calculation for how far laterally (relative to the plane's track) away from your original photographing position, would you have to have been, to have the moon appear shifted one diameter sideways.
The answer is 57 metres - not very much!
This is simply (diameter of moon) x (height of plane)/(height of moon)
= approx. 3474 km x 6.5 km / 395,000 km
This does not take into account your own altitude, which I think was around 500 m ASL. The answer would then be around 53 metres.
Note that these answers are of the same order of magnitude as those calculated by Dennis, however I have worked out the answer to a slightly different question: For a fixed plane position, how far sideways do you have to move to have the moon appear to shift one diameter?
Regarding the consistency of flight routes, there are standard routes between well-defined navigation points but a certain tolerance is allowed, and permission can be sought to move left or right of track to avoid weather cells. There would be a probability distribution for the plane to line up with the moon, such that every so often, the two would align, as has been perfectly captured by your picture.
Cheers,
Chris
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