The solution is pleasantly simple, just tell Apache to exempt this file from the authentication. This is fairly simple to do, and I added this FilesMatch block of code to my .htaccess:
# Exclude the file upload script from authentication
<FilesMatch "(async-upload\.php)$">
Satisfy Any
Order allow,deny
Allow from all
Deny from none
</FilesMatch>
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WordPress and basic authentication, problems with WP Cron and file uploads « ... - 0 views
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