Don't use CloudFlare ... and think that is a major factor with your issue. However, CloudFlare is done via DNS 'trickery' which forces all traffic (in or out) to you Moodle through CF *if* one uses the FQDN of the server. Don' think use of CF involves actual routing, however, thus .... a question and then a suggestion.
Can you access your Moodle server by IP address - not with a browser - but with other tools to get files to it?
Reason I ask .... the issue you've described does involve the acceptance of files + the processing on the Moodle end IF using the Moodle UI and using the Moodle UI would be by FQDN (DNS) and thus CF always involved.
What IF, one could access the server via IP and Xfer your zips (miniweb sites) to a file system repo in moodledata/repository/'nameofminisite'/ Since I use Mac/Linux server, 'scp' comes to mind for xfer and via ssh into server by IP one could then un-zip the 'minisite' uploaded.
That way 'minisite' files are there and only step remaining is the setup in Moodle Admin UI.
'spirit of sharing', Ken