i think what's going on is the normalization in ImageIntegration is getting thrown off by the gradient in the image. bad normalization for whatever reason == II has a hard time knowing what is truly an outlier across all the images.
i only stacked your blue "2" files, but first i opened them all and did a LinearFit with image 1 as the reference, then saved them. then in imageIntegration, i turned off normalization for both the stacking and rejection.
i suspect if you flattened these images the result might be better without the LF, but i'm not totally sure of that. another approach would be to DBE the images before going into II, but flats would be better.
anyway the result is better, but still not perfect. maybe it would improve if i threw in the "1" images as well.
rob