Which is why cross processing produces "experimental" results -- E6 is a CD-3 based process, as well, so E-6 film processed as a positive with a first developer and C-41 color dev will produce slightly off colors. Not greatly off, but not quite there.
FWIW, I've abandoned home mixing C-41 chemistry for now -- I bought a set of Flexicolor chems and I'm testing replenishment (processing to minimize oxygenation of the developer, and watching negatives carefully for changes in contrast, color shifts, or crossover as the developer ages).