Soot stains on Alpha jacket

I had went on a trip, we had a fire and it was windy so i wore my jacket. Initially, there was minor soot marks on the jacket. So i thought, no big deal, i'll throw it in the wash with some tech wash.

Big fuck up. The soot stain just spread throughout the jacket. Upon agitation, it just spreads across the fabric and doesn't lift. I tried to soak it in tech wash to attempt to remove it. It didn't lift again. I also tried dawn dish soap. It still didn't lift. I use the jacket for mountaineering and climbing, so cosmetic defect wouldn't totally destroy me. Its an orange jacket so its quite noticeable though.

What do fellas you suggest i try? Is there a way to even dye it if all fails? It is currently in the wash again so i can't attach a photo just yet. But i will after i take it out.