I’ve reviewed the ticket and it appears the team has been providing quite a bit of assistance and helping to troubleshoot issues which are well beyond the scope of Cloudflare’s settings. I appreciate that you are having difficulty but the issues appear to be primarily related to your server/ service migration and not Cloudflare specifically.
At the moment your DNS nameserver is not returning a response for www.your.domain. If your nameserver isn’t returning a response, then clients can’t be directed to Cloudflare. Since you are in a CNAME setup that means you’ve chosen to manage your own authoritative nameserver instead of using Cloudflare for DNS.
Other than it used to be that way before, is there any reason that you NEED to be in a CNAME setup and simply don’t use Cloudflare for authoritative DNS? It’s generally much easier to manage a full setup using Cloudflare.
At the moment with the current config there’s not really anything Cloudflare can do. You need to modify your current DNS provider’s settings for www so that it returns the correct value (e.g. www.your.domain.cdn.cloudflare.net).