Infact, meanwhile you are getting CloudFlare being implemented, do one more separate test.
There is a free site, that offers to create Moodle Sites for free. www.gnomio.com
They are hosted on Hetzner Online Servers (Germany) and are as well using nginx as their webserver, create account there, upload your course there and then access your course from there too just to see if it makes difference. This test can be done meanwhile you are waiting for cloudflare to cache content of your moodle site.