Would it work if you replaced “he” or “she” with “candidate” and “his” or “her” with “candidate’s” or with “their”?

That will prevent errors of concord (everything remains singular so you don’t have to change the verbs) and the sentences will mostly flow fine.

Your example would become: “Candidate is an esteemed archaeologist and writer based in Greece. Candidates’s (or “their”) primary residence is Athens, but they spend much of their time in Marrakech.