If it comes to that the marketplace is the place to take it.
As I said above, Discourse only needs one rule at cloudflare. That rule is:
You don’t want anything interfering with the javascript or how the page is loaded, which minification and rocket loader will do. Both usually end up with the issue you’re reporting.
If you want to cache assets then only turn that on after proving the site works with the above, and even then only use standard caching with /uploads/* - caching other stuff isn’t supported.
Knowing the FQDN helps us use other tools to look, but as we don’t have it we will skip that stage entirely.
That should be the only rule touching your site. If you have any others which risk overlapping then for now just shut them off.
If that doesn’t work then it’s time to look at apps.
Because your upgrade triggered the problem though it’s also still possible this is due to an old plugin. You said your install is bone stock, but do you mean just in terms of customisations? Are there any plugins added to the app.yml beyond the defaults? Broken plugins are also going to rear their heads during an upgrade.