Hi Luke,
I haven't done much with Tesseract for a while, but I updated the C
API a few years ago, and it was really straightforward to do. It's a
very light wrapper around Tesseract, so it should be easy to update
yourself if needed.
That said, I haven't kept up with recent development, so I may be
out of date, but I suspect it's still quite straightforward.
Best,
Nick