I couldn’t have done this without help from these people.
Thanks to Tom Taylor for making the request (and putting postboxes on iamnear.net using my ‘API’), Edward Betts for parsing it into TSV, Nick Burch for help and suggestions, OpenStreetMap for maps and postbox/ post office seeding, Abi Broom for requesting the last collection times, and Peter Chamberlin for making a further request.