“something weird associated with frame stacking”. Ah, I wonder if perhaps some frames have become rotated with respect to the others? If your stacking performs only rectilinear shifts then those near the center of rotation will be stacked perfectly but those further away will be smeared into short arcs. Removing a circularly symmetric synthetic star from the center of an arc will result in wings.
Could you try stacking, say, half the images and see if the result changes? Repeat with a differently chosen half, and again.