Classify big changes in target variable
I can only offer comments base on your statements. First of all,set your goal clear and straight. I think it is the maximization of BigChange and Flat Sensitivities .

I think Number 2 is problematic because of your concern of upcoming images. Classification is not Regression. There is a chance that model will never have a clue about the middle ranges. But you can set the classification threshold for flat and big change prediction for maximum sensitivities. The remaining unclassified images will be middle range changes. The problem here is that there could be a lot of mixed-ups from two different thresholds and unusual metric.

So I think 3 wins because 1 doesn't care if it is small or middle range changes. It is the most straightforward thing towards your goal. Note that even if you are classifying with 3 things the metric for optimization can just involve two things. But you should verify it. I think it is all right to compare the two remaining models. Cross validate and choose the winner base on combined sensitivity metric (including only flat and big changes). Just don't be fooled by randomness in selection.

You might just cross validate three models in the end just to be sure and always keep in mind the unusual metric for optimization. In addition, you should always remember classification thresholding (not target thresholding) for all models and there can always be a choice of no classification for some examples after thresholding. 

I'll be happy if you share the result of your experimentation and verify my hunch if it is wrong or not.