update: it worked! and no beety flava! i used the "fluffy buttercream icing" recipe from vegan cupcakes take over the world, and just microplaned about half a beet in batches, picking up about 1/2 a teaspoon of the grated beet at a time and squeezing it over the frosting while it mixed in my mixer (alternatively, you could certainly just add it in at any point if mixing manually.)
the pink i went with was a very girly baby pink, but there was lots of room to go deeper if i wanted to -- i am excited to experiment with different shades of beet -- purples, true reds -- the one i used was sort of wine coloured.
i refuse to eat food colouring, so am very happy to have the option of pink icing back in my life. i'm not even a huge fan of not chocolate icing, but i am a huge fan of making girly birthday cakes, so this is a big deal for me. try it!