Cut a few swatches of your darker fabric and try dyeing it with all 3 of your RIT dyes. Keep track of how much dye you use, what temperature the water is, and how long it sits in the dye bath. If none of the colors look right, change one of those variables and try again.
I've got lots of test swatches for my projects, along with notes about the mass of dye to mass of fabric, the time for dyeing, and the amounts of any other compounds added. Now, I'm an organic chemist and got in the habit of keeping a detailed lab notebook years ago. It does get me repeatable results with the exact colors I want, so I think it's worth the fussiness.
For your specific dyes, my inclination would be to try a mix of scarlet and petal pink; I think that might give you the darker pink-red color you want. But I've never used those dyes, so experiment!
(also, Avatar: the Last Airbender cosplayers represent! I do Zuko a lot. ^_#)