Now that you have already applied dye; I don't know if this will work......but it's worth a try.
I have an older American Eagle with the fabric(carpet) ceiling covering. I once had a leak around the skylight which caused a brown stain. Somewhere online, I found a video of someone spraying oxyclean in solution directly onto a similar stain. Within seconds, the stain magically disappeared.
So, I bought a tub of oxyclean, mixed it with water until dissolved, then put it in a clean spray bottle. From that point, it took me a solid thirty seconds to completely eradicate the brown spot. Just spray until lightly soaked and watch the magic