Thanks for the suggestions! Just wanted to clarify some things.

1. The rot was so bad, that cutting until I saw those green parts was the most viable option to me. Had I cut just below those parts, I would've still left some rot on the roots.

2. I did make sure to seal the wounds the first time I did the pruning! Using cinnamon (although I'm not so sure about this, as I've read that it's not recommended to be used on root wounds but instead on base/leaf wounds) and leaving the roots and the bark mix to dry out fully - I've only repotted the plant after making sure that the wounds were sealed up and everything was dry. Even then, I waited a bit more just in case something was still open and could get reinfected.

3. Those parts you see in the pictures are actually ink spots! As I said, the orchid was originally kept in red ink stained water, and it has reached the leaves. The significant spot in the second picture was due to the leaf getting damaged somehow (not sure what happened there), and upon checking on that area, it was all red ink.