Repotting Psychopsis HELP!

[Syrinth]

Hello everyone, so I have a Psychopsis Papillio that I bought at our orchid show last April that desperately needs to be repotted.

It's extremely rootbound, and has one pseudobulb that is hanging outside of the pot. Additionally, the thin plastic pot is starting to break near where the pseudobulb is hanging out.

I know it needs repotting, but I've been putting it off. Now, however, another pseudobulb is forming and I think this needs to be done ASAP.

How do I do this without killing the plant? I've heard Psychopsis are hard to repot. It's currently in flower if that matters.