How would you go about converting a reasonably large (>300K), fairly mature C codebase to C++?
The kind of C I have in mind is split into files roughly corresponding to
Probably two things to consider besides how you want to start are on what you want to focus, and where you want to stop.
You state that there is a large code churn, this may be a key to focus your efforts. I suggest you pick the parts of your code where a lot of maintenance is needed, the mature/stable parts are apparently working well enough, so it is better to leave them as they are, except probably for some window dressing with facades etc.
Where you want to stop depends on what the reason is for wanting to convert to C++. This can hardly be a goal in itself. If it is due to some 3rd party dependency, focus your efforts on the interface to that component.
The software I work on is a huge, old code base which has been 'converted' from C to C++ years ago now. I think it was because the GUI was converted to Qt. Even now it still mostly looks like a C program with classes. Breaking the dependencies caused by public data members, and refactoring the huge classes with procedural monster methods into smaller methods and classes never has really taken off, I think for the following reasons:
NB. I suppose you know the "Working effectively with Legacy code" book?