Yes, using a tiny bit of something black will get you red color. Carafa is a good choice since it won't give you much flavor.
Rather than adding it to the mash as part of the sparge, why don't you do something where you can see the color more directly? You could either steep the carafa in the sparge water directly, or in the wort after it's in the kettle. Put it in a mesh bag and just dunk it in there until you get the color you want.
You can repeat this process if it's hard to tell the color directly. Dunk, remove, stir, sample, repeat. If you are going to evaluate the color, it's hard to eyeball it in one of the brewing vessels. Take it out and put it in a pint glass so you can tell what the drinker will see.