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I can't quite figure out the differences between these two. I would guess that 食料 is only used in situations, where the only thing that matters is that the food is there or not there (As in, searching for food, gave food, need food)
I've only seen 食品 used in connection to the process of making, acquiring, selling and storing the food.
Am I on the right track here, or completely off?
You are on the right track. They are almost the same meaning, however 食品 is generally used for manufacturer products or food that consumers buy (the end product) (商品). 食料, as implied by the 料, implies the base materials, i.e. the stuff used to make 食品. Also, note that 食料 does not include 主食 (which is an important concept in Japan), while 食糧 is generally used to mean 主食 (rice, wheat, etc.).
食糧to the mix?