In the question - "Nonetheless, there are opinions that permit partial depictions (see, e.g., Shach YD141:25, Neharei Afarsamon YD 118, and Darkhei Teshuva 141:40 cited here)."
A little farther down in that link I found -
May one draw a picture of a forbidden form, or take/develop the picture from a camera?
It is forbidden to draw the above forms in a complete way, as stated above in B. Accordingly, it would be forbidden to take or develop a picture of the sun, moon or stars unless it is being done for educational purposes. Those however who are lenient in this matter have upon whom to rely.
 As a) Some Poskim rule a mere drawing is permitted. b) One is not actually drawing the picture and is simply having the camera do so for him based on his command. Now, although this is a classical case of Kocho, which is forbidden, nevertheless, when added to the previous reason it seemingly carries greater leniency.
So it would seem that in regard to the question of "is one allowed to photograph and/or own a photograph of an eclipse?" That there is room to be מקיל.