I'd recommend making it white or green, just like all the other fabric, but with a single twist: some turquoise blue runes or markings on it. That way, it still pops because it complements the rest, but you're not making the sash stick out like a sore thumb.
That said, Red isn't a bad idea, especially if you start from a purplish base and build to red, to keep a cooler color scheme. If you do the same colors on the eyes, you'll have some nice balance.
Finally, a piece of advice is to ignore the codex. It's hard and I have trouble doing it too, but everything in there is a suggestion. My Biel-Tan are blue-grey and jade rather than white and green, I paint Space Wolves a more neutral grey, my Salamanders end up a good deal darker than Snot Green, etc.
But if you feel like something needs a change, try out something new. I don't know if you're using a metal figure or not, but if you are, experiment. The worst that happens is you strip it of paint, you lose some hours of painting, but you gain experience. Try something bold and push yourself. Or, just paint it like the rest of the fabric. Exterior of the cloak color, or something. Not every detail needs to be emphasized; some things are just decorative.
