aha! the idea in my head is screwing plasterboard to the current wood door lining and skimming on top of that, then the gap can be filled and a corner bead used atop
I'd be reticent to remove the wood frame in case there's anything semi-structural. It can't go ontop. As the skiritng is on, and from a timings pov I won't be able to do everything required.
I'll post some more pics as I'm struggling to work out your suggestion.
The issue is the frame is wood and you can't plaster on top of it.
Here is a birds eye view of the issue.
At the moment the wood frame is flush. But after the skim it'll be too low.