Heat and vinegar took Hawaiian Punch stains out of my beige carpet. Just soak a white cloth in vinegar, lay it on the stain and iron it. Just like using vinegar to color eggs. The color leeches on to the cloth, rinse frequently in cold water and resaturate cloth after each rinse. It took a little while, but the stain is gone. Iron was set on warm.
Try leaving a good dollop of shaving foam on the spot then leave for a while. Go back with a damp sponge and see if that lifts it out. I use shaving foam on my carpets- even though i haven't tried it with food colouring-it might be worth trying. Good luck and good luck with your move!
I have had good luck with a retail product called Spot Shot carpet cleaner. It took out a month old tea spill stain from my light carpet. I've never tried it on food coloring, but it has taken everything else out of my carpet such as tea, coffee, soda, tar, and dirt. Good luck!
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