Ok, I'm back from some reading up, and I learned that Blue Red Splash does NOT mean a splash version of red. It just means a black breasted red wherein the black areas are either blue or splash. And the red is mostly unaffected.
And I also learned that the effect of the blue-splash genes on these red birds can mimic the effect of Dominant White, so that the Blue Red Splashes and Red Pyles look very similar to each other.
That explains why my hen looks like both. But she can't be a Splash, because then all of her chicks, when mated to the CL rooster, would be blues, but they are not.