I tried dyeing again - this time with German food colouring. Because food colouring doesn't contain citric acid, like Kool Aid does, I had to replace it with vinegar. Lots of vinegar. Lots and lots and lots of vinegar. The whole house smelled like a pickling plant, and it smelled of pickles for days.
But the initial results were pleasing:
Unfortunately, having these hanks of wool about made our house smell like a Fish'n'Chip shop (and at this point I would like to note that the Kool Aid yarn now smells faintly fruity and entirely pleasing), so I had to wash them before I wound them into skeins. And then disaster struck: the colours - already muted - washed out. Now the yarn looks tired and faded, and I'll have to re-dye it. With Kool Aid.
See? I'm a convert. Or a Konvert, more like.