I don't know if this is the recommended method, but I would first copy the books from the Kindle to a folder on the computer (how you do that depends on your system; in Windows, it's a straight drag-and-drop). Then drag the corresponding files from that folder into Calibre.
Of course, there might be DRM issues, but that's another matter.
As for Calibre not being fit for purpose, that depends on what you think its purpose is. I use it to keep track of my book collection, and also to edit the metadata and sometimes change the books' covers. For those purposes, it is extremely fit.
Mike
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