The site was then successfully accessible on the internet, though I did notice that the full path had to be entered in the browser address bar, including the page name itself - for example, https://[siteurl]/default.aspx rather than just https://[siteurl].
Further testing revealed that the links in the breadcrumbs all led to a "Page cannot be diaplayed" IE error, and submitting a search on the site gave an error message on the results page that stated:
The cause was all in the AAM entry - I had a port number (80) in the extranet URLs from some early trials, and had not removed this port number when setting https. By setting the Extranet zone AAM internal URL and public URL to be simply https://[ssiteurl], these problems were solved.
Interesting that the pages were still accessible with an incorrect Access Mapping!