FWIW, I have white binding on that PRS build above and no problem scraping it clean after using alcohol dyes.As you have binding on your guitar, avoid alcohol based stain. It will get deep into all the tiny stress cracks in the binding that you can't see. Water-based stain is less penetrating and may sit on the top the larger cracks but can be scraped off.
I did mask it well and it didn't bleed too badly. Maybe because the top was amber and only the sides/back were red also has something to do with it. When I did the top & sides, it was elevated and laying flat (front up). The amber is less prominent than red, and maybe there was not enough capillary action for the red to go up. Dunno...
We all have different experiences and results.